IIT-JEE 1998 | Circle Question 49 | Mathematics

IIT-JEE 1998

MCQ (More than One Correct Answer)

-0.5

The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is

IIT-JEE 1998

MCQ (More than One Correct Answer)

-0.5

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

$${x_1}\, + \,{x_2} + \,{x_3}\, + \,{x_4}\, = 0$$

$${y_1}\, + \,{y_2} + \,{y_3}\, + \,{y_4}\, = 0$$

$${x_1}\,{x_2}\,{x_3}\,{x_4}\, = {c^4}$$

$${y_1}\,{y_2}\,{y_3}\,{y_4}\, = {c^4}$$

IIT-JEE 1988

MCQ (More than One Correct Answer)

-0.5

The equations of the tangents drawn from the origin to the circle $${x^2}\, + \,{y^2}\, - \,2rx\,\, - 2hy\, + {h^2} = 0$$, are

x = 0

y = 0

$$({h^2}\, - \,{r^2})\,x - \,\,2rhy\, = \,0$$

$$({h^2}\, - \,{r^2})\,x + \,\,2rhy\, = \,0$$

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