The straight lines joining any point `P` on the parabola `y^2=4a x` to the vertex and perpendicular from the focus to the tangent at `P` intersect at `Rdot` Then the equation of the locus of `R` is
(a)`x^2+2y^2-a x=0` (b)`2x^2+y^2-2a x=0` (c)`2x^2+2y^2-a y=0` (d) `2x^2+y^2-2a y=0`

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) in the ratio 1:3. Then the locus of P is :

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is (a) x^2+y^2=5 (b) sqrt(5)(x^2+y^2)-3x-4y=0 (c) sqrt(5)(x^2+y^2)+3x+4y=0 (d) x^2+y^2=25

From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is drawn & extended to a M point such that AM=2AB. The equation of the locus of M is: (A) x^2 +8x+y^2 =0 (B) x^2+8x+(y-3)^2=0 (C) (x-3)^2+8x+y^2=0 (D) x^2+8x+8y^2=0