## Question

The vertex of the parabola *y*^{2} = 8*x* is at the center of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is

### Solution

*x*^{2} +* y*^{2} = 20

Vertex = (0, 0). The ends of latus rectum are (2, 4), (2, – 4)

.

#### SIMILAR QUESTIONS

The line will touch the parabola *y*^{2} = 4*a*(*x + a*), if

The equation of the parabola whose axis is vertical and passes through the points (0, 0), (3, 0) and (–1, 4), is

The points on the parabola *y*^{2} = 36*x* whose ordinate is three times the abscissa are

The points on the parabola *y*^{2} = 12*x* whose focal distance is 4, are

Axis of the parabola *x*^{2} – 4*x* – 3*y *+ 10 = 0 is

The equation of the latus rectum of the parabola *x*^{2} + 4*x* + 2*y *= 0 is

*x* – 2 = *t*^{2}, *y* = 2*t* are the parameter equations of the parabola

The equation represents a parabola if is

‘*t*_{1}’ and ‘*t*_{2}’ are two points on the parabola *y*^{2} = 4*x*. If the chord joining them is a normal to the parabola at ‘*t*_{1}’ then

Find the equation of the parabola whose focus is (1, 1) and the directrix is *x + y *+ 1 = 0.