LONG ANSWER QUESTIONS (7 MARKS)
STRAIGHT LINE
1. Find the circumcentre of the triangle whose vertices are (2, 3), (2, 1) and (4, 0).
2. Find the circumcentre of the triangle whose vertices are (1, 3), (3, 5) and (5, 1).
3. Find the circumcentre of the triangle whose sides are given by
x + y + 2 = 0, 5x y 2 = 0 and x 2y + 5 = 0.
4. Find the circumcentre of the triangle formed by the straight lines
x + y = 0, 2x + y + 5 = 0 and x y = 2.
5. Find the orthocentre of the triangle whose vertices are (5, 7), (13, 2), (5, 6).
6. Find the orthocentre of the triangle with the vertices (-2, -1), (6, -1) and (2, 5).
7. If the equation of the sides a triangle are 7x + y 10 = 0, x 2y + 5 = 0 and x + y + 2 = 0,
find the orthocentre of the triangle.
8. Find the orthocentre of the triangle formed by the lines
x + 2y = 0, 4x + 3y 5 = 0 and 3x + y=0.
9. Find the equations of the straight line passing through the point (1, 2) and making an angle of
60° with the line 3x y 2 0 .
10. The base of an equilateral triangle is x + y 2 = 0 and the opposite vertex is (2, 1). Find the
equations of the remaining sides.
11. Find the equations of the straight lines passing the point of intersection of the lines
3x + 2y + 4 = 0, 2x + 5y = 1 and whose distance from (2, -1) is 2.
LOCUS
1. If the distances from P to the points (5, 4) and (7, 6) are in the ratio 2 : 3, then find the
equation of locus of P.
2. A(5, 3) and B(3, 2) are two fixed points. Find the equation of locus of P, so that the area of
triangle PAB is 9.
3. A(2, 3) and B(3, 4) are two fixed points. Find the equation of locus of P, so that the area of
triangle PAB is 8.5.
4. Find the equation of locus of P, if the line segment joining (2, 3), (1, 5) subtends a right
angle at P.
5. A(1, 2), B(2, 3) and C(2, 3) are three points. A point ‘P’ moves such that PA2 + PB2 = 2PC2.
Show that the equation to the locus of ‘P’ is 7x - 7y + 4 = 0
6. Find the equation of locus of P, if A = (2, 3), B(2, 3) and PA + PB = 8.
TRANSFORMATION OF AXES
7. If the transformed equation of a curve is X2 + 3XY 2Y2 + 17X 7Y 11 = 0. when the origin
is shifted to (2, 3). Find the original equation of the curve.
8. Find the transformed equation of 3x2 + 10xy + 3y2 = 9 when the axes are rotated through an
angle /4.
9. Find the transformed equation of x2 + 2 3 xy y2 = 2a2 when the axes are rotated through
an angle /6.
10. Find the transformed equation of x cos + y sin = p when the axes are rotated through an
angle .
11. When the axes are rotated through an angle 450, the transformed equation of a curve is 17X2
16XY + 17Y2 = 225. Find the original equation of the curve.
STRAIGHT LINE
12. Find the points on the line 3x 4y1=0 which are at a distance of 5 units from the point(3, 2).
13. A straight line through Q( 3, 2) makes an angle with the positive direction of x-axis. If the
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straight line intersects the line 3x - 4y + 8 = 0 at P, find the distance PQ.
14. A straight line with slope 1 passes through Q (3,5) and meets the straight line x + y 6 = 0
at P. Find the distance PQ.
BY IRFAN SIR 9030818319
15. A straight line through Q(2, 3) makes an angle 3/4 with negative direction of the x-axis. If
the straight line intersects the line x + y 7 = 0 at P. Find the distance PQ.
16. Find the value of ‘k’ if the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are
concurrent.
17. Find the values of k,if the angle between the straight lines 4x-y + 7 =0 and kx -5y-9=0 is 450.
BY IRFAN SIR 9030818319
