1

IIT-JEE 1999

Subjective

+10

-0

Consider the family of circles $${x^2} + {y^2} = {r^2},\,\,2 < r < 5$$. If in the first quadrant, the common taingent to a circle of this family and the ellipse $$4{x^2} + 25{y^2} = 100$$ meets the co-ordinate axes at $$A$$ and $$B$$, then find the equation of the locus of vthe mid-point of $$AB$$.

2

IIT-JEE 1998

Subjective

+8

-0

The angle between a pair of tangents drawn from a point $$P$$ to the parabola $${y^2} = 4ax$$ is $${45^ \circ }$$. Show that the locus of the point $$P$$ is a hyperbola.

3

IIT-JEE 1997

Subjective

+5

-0

A tangent to the ellipse x

^{2}+ 4y^{2}= 4 meets the ellipse x^{2}+ 2y^{2}= 6 at P and Q. Prove that the tangents at P and Q of the ellipse x^{2}+ 2y^{2}= 6 are at right angles.4

IIT-JEE 1996

Subjective

+3

-0

Points $$A, B$$ and $$C$$ lie on the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$A, B$$ and $$C$$, taken in pairs, intersect at points $$P, Q$$ and $$R$$. Determine the ratio of the areas of the triangles $$ABC$$ and $$PQR$$.

Questions Asked from Conic Sections (Subjective)

Number in Brackets after Paper Indicates No. of Questions

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