## Question

The line* x – y* + 2 = 0 touches the parabola *y*^{2} = 8*x* at the point

### Solution

(2, 4)

*y*^{2} = 8*x* … (1)

*x – y* + 2 = 0 … (2)

(1) and (2) *y*^{2} = 8(*y* – 2)

Now (2), *x – y* + 2 = 0 *x* = 2.

#### SIMILAR QUESTIONS

The length of the subnormal to the parabola *y*^{2} = 4*ax* at any point is equal to

The slope of the normal at the point (*at*^{2}, 2*at*) of parabola *y*^{2} = 4*ax* is

Equation of locus of a point whose distance from point (*a*, 0) is equal to its distance from y-axis is

Through the vertex *O* of parabola *y*^{2} = 4*x*, chords *OP* and *OQ* are drawn at right angles to one another. The locus of the middle point of *PQ *is

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola *y*^{2} = 4*ax* is another parabola with directrix

The equation of common tangent to the curves *y*^{2} = 8*x* and *xy* = –1 is

From the point (–1, 2) tangent lines are drawn to the parabola *y*^{2} = 4*x*, then the equation of chord of contact is

For the above problem, the area of triangle formed by chord of contact and the tangents is given by

A point moves on the parabola *y*^{2} = 4*ax*. Its distance from the focus is minimum for the following value(s) of *x*.

If *t* is the parameter for one end of a focal chord of the parabola *y*^{2} = 4*ax*, then its length is