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1

JEE Advanced 2013 Paper 2 Offline

MCQ (More than One Correct Answer)
Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length $$2\sqrt 7 $$ on y-axis is (are)
A
$${x^2}\, + \,{y^2}\, - \,6x\,\, + 8y\, + 9 = 0$$
B
$${x^2}\, + \,{y^2}\, - \,6x\,\, + 7y\, + 9 = 0$$
C
$${x^2}\, + \,{y^2}\, - \,6x\,\, - 8y\, + 9 = 0$$
D
$${x^2}\, + \,{y^2}\, - \,6x\,\,- 7y\, + 9 = 0$$
2

IIT-JEE 1998

MCQ (More than One Correct Answer)
If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}),\,Q\,\,({x_2},\,{y_2}),\,\,R\,({x_3},\,{y_3}),\,S\,({x_4},\,{y_4}),$$ then
A
$${x_1}\, + \,{x_2} + \,{x_3}\, + \,{x_4}\, = 0$$
B
$${y_1}\, + \,{y_2} + \,{y_3}\, + \,{y_4}\, = 0$$
C
$${x_1}\,{x_2}\,{x_3}\,{x_4}\, = {c^4}$$
D
$${y_1}\,{y_2}\,{y_3}\,{y_4}\, = {c^4}$$
3

IIT-JEE 1998

MCQ (More than One Correct Answer)
The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is
A
0
B
1
C
3
D
4
4

IIT-JEE 1988

MCQ (More than One Correct Answer)
The equations of the tangents drawn from the origin to the circle $${x^2}\, + \,{y^2}\, - \,2rx\,\, - 2hy\, + {h^2} = 0$$, are
A
x = 0
B
y = 0
C
$$({h^2}\, - \,{r^2})\,x - \,\,2rhy\, = \,0$$
D
$$({h^2}\, - \,{r^2})\,x + \,\,2rhy\, = \,0$$

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