Analytical geometry - Combination problems

Problems that require concepts from two or more chapters

The radius of the circle passing through the foci of the ellipse

x²/16 + y²/9 = 1 and having its centre at (0,3) is

a. 4
b. 3
c. √12
d. 7/2

JEE 1995

Hyperbola - Past JEE

If x = 9 is the chord of contact of the hyperbola x²-y² = 9, then the equation of the corresponding pair of tangents is

a. 9x² -8y² +18x-9 = 0
b. 9x² -8y² -18x+9 = 0
c. 9x² -8y² -18x-9 = 0
d. 9x² -8y² +18x+9 = 0

(JEE 1999)

Answer: b.

The chord of contact x =9 meets the hyperbola at (9,6√2) and (9,-6√2).
the equations of tangent at these points are 3x-2√(2y)-3 = 0 and 3x+2√(2y)-3 = 0.
the combined equation of the two is:

9x² -8y² -18x+9 = 0