11th Maths Monthly Test - 4 ( Two Dimensional Analytical Geometry )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Two Dimensional Analytical Geometry )-Aug 2020

Time : 2.30 Hours

Part - A

Generic 5 - Answer All Question

The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and
(iii) Find the value of F for 38°C.

If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2, then find the equation of the line.

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.

Show that the equation 2x² - xy - 3y² - 6x + 19y - 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is \(\tan ^{ -1 }{ \left( 5 \right) } \)

Rewrite √3x+y+4=0 in to normal form.

Find the equation of the perpendicular bisector of the line segment joining the points (1, 1) and (2, 3).

The quantity demanded of a certain type of Compact Disk is 22,000 units when a unit price is Rs.8. The customer will not buy the disk, at a unit price of Rs.30 or higher. On the other side the manufacturer will not market any disk if the price is Rs.6 or lower. However, if the price Rs.14 the manufacturer can supply 24,000 units. Assume that the quantity demanded and quantity supplied are linearly proportional to the price. Find (i) the demand equation (ii) supply equation (iii) the market equilibrium quantity and price. (iv) The quantity of demand and supply when the price is Rs.10.

Find the equation of the lines passing through the point (1,1)
(i) with y-intercept (-4)
(ii) with slope 3
(iii) and (-2, 3)
(iv) and the perpendicular from the origin makes an angle 60° with x- axis.

Find p and q, if the following equation represents a pair of perpendicular lines 6x² + 5xy - py² + 7x + qy - 5 = 0.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x² + 5xy - 2y² + 4x + 5y = 0 are at right angles.

The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

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11th Maths Monthly Test - 4 ( Two Dimensional Analytical Geometry )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Two Dimensional Analytical Geometry )-Aug 2020

Part - A

Generic 5 - Answer All Question

The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F. (i) Find the linear relationship between C and F. (ii) Find the value of C for 98.6°F and (iii) Find the value of F for 38°C.

If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2, then find the equation of the line.

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using (i) concept of slope (ii) a straight line (iii) any other method.

Show that the equation 2x2 - xy - 3y2 - 6x + 19y - 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is \(\tan ^{ -1 }{ \left( 5 \right) } \)

Rewrite √3x+y+4=0 in to normal form.

Find the equation of the perpendicular bisector of the line segment joining the points (1, 1) and (2, 3).

Find the equation of the lines passing through the point (1,1) (i) with y-intercept (-4) (ii) with slope 3 (iii) and (-2, 3) (iv) and the perpendicular from the origin makes an angle 60° with x- axis.

Find p and q, if the following equation represents a pair of perpendicular lines 6x2 + 5xy - py2 + 7x + qy - 5 = 0.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0 (i) through the point (-1, 2) (ii) Parallel to x - y + 5 = 0 (iii) Perpendicular to x - 2y + 1 = 0.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x2 + 5xy - 2y2 + 4x + 5y = 0 are at right angles.

The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

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Tamilnadu Stateboardszs - Class

The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and
(iii) Find the value of F for 38°C.

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.

Show that the equation 2x² - xy - 3y² - 6x + 19y - 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is \(\tan ^{ -1 }{ \left( 5 \right) } \)

Find the equation of the lines passing through the point (1,1)
(i) with y-intercept (-4)
(ii) with slope 3
(iii) and (-2, 3)
(iv) and the perpendicular from the origin makes an angle 60° with x- axis.

Find p and q, if the following equation represents a pair of perpendicular lines 6x² + 5xy - py² + 7x + qy - 5 = 0.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x² + 5xy - 2y² + 4x + 5y = 0 are at right angles.