1

IIT-JEE 1993

Subjective
Find the coordinates of the point at which the circles $${x^2}\, + \,{y^2} - \,4x - \,2y = - 4\,\,and\,\,{x^2}\, + \,{y^2} - \,12x - \,8y = - 36$$ touch each other. Also find equations common tangests touching the circles in the distinct points.

Answer

$$\left( {{{14} \over 5},{8 \over 5}} \right),\,\,y = 0$$ and $$7y - \,24x\, + \,16\, = 0$$
2

IIT-JEE 1992

Subjective
Let a circle be given by 2x (x - a) + y (2y - b) = 0, $$(a\, \ne \,0,\,\,b\, \ne 0)$$. Find the condition on a abd b if two chords, each bisected by the x-axis, can be drawn to the circle from $$\left( {a,\,\,{b \over 2}} \right)$$.

Answer

$${a^2}\, > \,2\,{b^2}$$
3

IIT-JEE 1991

Subjective
Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y = 10, find the equation of the circles.

Answer


$${x^2}\, + \,{y^2} + 6x\, + 2y - 15\, = 0$$ and
$${x^2}\, + \,{y^2} - 10x\, - 10y + 25\, = 0$$
4

IIT-JEE 1990

Subjective
A circle touches the line y = x at a point P such that OP = $${4\sqrt 2 \,}$$, where O is the origin. The circle contains the point (- 10, 2) in its interior and the length of its chord on the line x + y = 0 is $${6\sqrt 2 \,}$$. Determine the equation of the circle.

Answer

$${x^2}\, + {y^2} + \,18x\, - 2y\, + 32\, = 0$$

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12