Conic Sections ...

A Iight ray gets reflected

from the $$x = -2$$. If the reflected touches the circle $$x^2 + y^2 = 4$$ and point of incident is $$(-2,-4)$$, then equation of incident ray is 

Find the equation of the circle with center at $$(-3,5)$$ and passes through the point $$(5,-1)$$

Normals $$AA,A{A}_{1}$$ and $$A{A}_{2}$$ are drawn to the parabola $${ y }^{ 2 }=8x$$ from the point $$A(h,0)$$. If triangle $$O{A}_{1}{A}_{2}$$ is equilateral , then the possible value of $$h$$ is

Consider a parabola $$P$$ which touches $$y = 0$$ at $$(1, 0)$$ and $$x = 0$$ at $$(0, 2)$$, then latus rectum of $$P$$ is,

A circle touches the y-axis at $$(0, 2)$$ and has an intercept of $$4$$ units on the positive side of the x-axis. Then the equation of the circle is?

Let $$S$$ be the focus of $${ y }^{ 2 }=4x$$ and a point $$P$$ be moving on the curve such that its abscissa is increasing at the rate of $$4 units/s$$. Then the rate of increase of the projection of $$SP$$ on $$x+y=1$$ when $$P$$ is at $$(4,4)$$ is

O is the centre of a circle of diameter $$4$$cm and OABC is a square, if the shaded area is $$\displaystyle\frac{1}{3}$$ area of the square, then the side of the square is __________.

The ratio of the areas of the triangle $$PQS$$ and $$PQR$$ is :

If eccentricity of both ellipses are same, then their eccentricity is

An endless inextensible string of length $$15$$m passes around the pins, A & B which are $$5$$m apart. This string is always kept tight and a small ring, R of negligible dimensions, inserted in this string is made to move in a path keeping all segments RA, AB, RB tight (as mentioned earlier). The ring traces a path, given by conic C, then.