12th Maths Weekly Test -1 (Two Dimensional Analytical Geometry-II)

St. Britto Hr. Sec. School - Madurai

12th Maths Weekly Test -1 (Two Dimensional Analytical Geometry-II)-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x²+y²−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

\(0,-\frac { 40 }{ 9 } \)
0
\(\frac { 40 }{ 9 } \)
\(\frac { -40 }{ 9 } \)

The circle x²+y²=4x+8y+5intersects the line3x−4y=m at two distinct points if

15< m < 65
35< m <85
−85<m < −35
−35<m <15

The equation of the normal to the circle x²+y²−2x 2y+1=0 which is parallel to the line
2x+4y=3 is

x+2y=3
x+2y+3= 0
2x+4y+3=0
x−2y+3= 0

The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
and x+2y=4 is

10
\( {2} \sqrt {5}\)
6
4

If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents
to the circle (x−3)²+(y+2)²=r² , then the value of r² is

The ellipse E₁\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E₂ passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is
\(\frac { \sqrt { 2 } }{ 2 } \)

\(\frac { \sqrt { 3 } }{ 2 } \)

\(\frac { 1 }{ 2 } \)

\(\frac { 3 }{ 4 } \)
The radius of the circle3x²+by²+4bx−6by+b² =0 is
1

3

\( \sqrt {10}\)

\( \sqrt {11}\)

The equation of the circle passing through the foci of the ellipse \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) having centre at
(0,3) is

x²+y²−6y−7=0
x²+y²−6y+7=0
x²+y²−6y−5=0
x²+y²−6y+5=0

Consider an ellipse whose centre is of the origin and its major axis is along x-axis. If its eccentrcity is \(\frac { 3 }{ 5 } \) and the distance between its foci is 6, then the area of the quadrilateral inscribed in the ellipse with diagonals as major and minor axis of the ellipse is

An ellipse hasOB as semi minor axes, F and F′ its foci and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

\(\frac { 1 }{ \sqrt { 2 } } \)
\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 4 } \)
\(\frac { 1 }{ \sqrt { 3 } } \)

If the two tangents drawn from a point P to the parabola y² = 4x are at right angles then the
locus of P is

2x+1=0
x = −1
2x−1=0
x =1

Part - B

Generic 2 - Answer All Question

Find the equation of circles that touch both the axes and pass through (-4,-2) in general form.

Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

A circle of area 9p square units has two of its diameters along the lines x+y=5 and x−y=1.
Find the equation of the circle.

Find the equation of the tangent and normal to the circle x²+y²−6x+6y−8=0 at (2,2) .
Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

Find centre and radius of the following circles.
x₂+ (y+2)² =0

Part - C

Generic 3 - Answer All Question

Find the circumference and area of the circle x² +y² - 2x + 5y + 7 = 0

Find the condition for the line lx + my + n = 0 is Rtangent to the circle x² + y² = a²

Find the equatlon of the ellipse whose e = \(\frac34\), foci ony-axl ,centre at origin and passing through (6,4).

Find the value of c if y = x + c is a tangent to the hyperbola 9x² - 16y² = 144.

Find the equation of the circle described on the chord 3x+y+5= 0 of the circle x²+y²=16 as diameter.
Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

Part - D

Generic 5 - Answer All Question

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Find the equation of the circle passing through the points(1,1), (2,-1) , and(3,2) .
The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x²−4x−5y−1=0.

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12th Maths Weekly Test -1 (Two Dimensional Analytical Geometry-II)

St. Britto Hr. Sec. School - Madurai

12th Maths Weekly Test -1 (Two Dimensional Analytical Geometry-II)-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

The circle x2+y2=4x+8y+5intersects the line3x−4y=m at two distinct points if

The equation of the normal to the circle x2+y2−2x 2y+1=0 which is parallel to the line 2x+4y=3 is

The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6 and x+2y=4 is

If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

The ellipse E1\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

The radius of the circle3x2+by2+4bx−6by+b2 =0 is

The equation of the circle passing through the foci of the ellipse \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) having centre at (0,3) is

Consider an ellipse whose centre is of the origin and its major axis is along x-axis. If its eccentrcity is \(\frac { 3 }{ 5 } \) and the distance between its foci is 6, then the area of the quadrilateral inscribed in the ellipse with diagonals as major and minor axis of the ellipse is

An ellipse hasOB as semi minor axes, F and F′ its foci and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

If the two tangents drawn from a point P to the parabola y2 = 4x are at right angles then the locus of P is

Part - B

Generic 2 - Answer All Question

Find the equation of circles that touch both the axes and pass through (-4,-2) in general form.

Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

A circle of area 9p square units has two of its diameters along the lines x+y=5 and x−y=1. Find the equation of the circle.

Find the equation of the tangent and normal to the circle x2+y2−6x+6y−8=0 at (2,2) .

Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

Find centre and radius of the following circles. x2+ (y+2)2 =0

Part - C

Generic 3 - Answer All Question

Find the circumference and area of the circle x2 +y2 - 2x + 5y + 7 = 0

Find the condition for the line lx + my + n = 0 is Rtangent to the circle x2 + y2 = a2

Find the equatlon of the ellipse whose e = \(\frac34\), foci ony-axl ,centre at origin and passing through (6,4).

Find the value of c if y = x + c is a tangent to the hyperbola 9x2 - 16y2 = 144.

Find the equation of the circle described on the chord 3x+y+5= 0 of the circle x2+y2=16 as diameter.

Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

Part - D

Generic 5 - Answer All Question

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Find the equation of the circle passing through the points(1,1), (2,-1) , and(3,2) .

The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x2−4x−5y−1=0.

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The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x²+y²−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

The circle x²+y²=4x+8y+5intersects the line3x−4y=m at two distinct points if

The equation of the normal to the circle x²+y²−2x 2y+1=0 which is parallel to the line
2x+4y=3 is

The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
and x+2y=4 is

If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents
to the circle (x−3)²+(y+2)²=r² , then the value of r² is

The ellipse E₁\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E₂ passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

The radius of the circle3x²+by²+4bx−6by+b² =0 is

The equation of the circle passing through the foci of the ellipse \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) having centre at
(0,3) is

If the two tangents drawn from a point P to the parabola y² = 4x are at right angles then the
locus of P is

A circle of area 9p square units has two of its diameters along the lines x+y=5 and x−y=1.
Find the equation of the circle.

Find the equation of the tangent and normal to the circle x²+y²−6x+6y−8=0 at (2,2) .

Find centre and radius of the following circles.
x₂+ (y+2)² =0

Find the circumference and area of the circle x² +y² - 2x + 5y + 7 = 0

Find the condition for the line lx + my + n = 0 is Rtangent to the circle x² + y² = a²

Find the value of c if y = x + c is a tangent to the hyperbola 9x² - 16y² = 144.

Find the equation of the circle described on the chord 3x+y+5= 0 of the circle x²+y²=16 as diameter.

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x²−4x−5y−1=0.