Question

The line x – y + 2 = 0 touches the parabola y2 = 8x at the point

Solution

Correct option is

(2, 4)

y2 = 8x               … (1)

x – y + 2 = 0      … (2)

(1) and (2)   y2 = 8(y – 2)

Now (2),  x – y + 2 = 0   x = 2.

SIMILAR QUESTIONS

Q1

The length of the subnormal to the parabola y2 = 4ax at any point is equal to

Q2

The slope of the normal at the point (at2, 2at) of parabola y2 = 4ax  is

Q3

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

Q4

Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is

Q5

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Q6

The equation of common tangent to the curves y2 = 8x and xy = –1 is

Q7

From the point (–1, 2) tangent lines are drawn to the parabola y2 = 4x, then the equation of chord of contact is

Q8

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

Q9

A point moves on the parabola y2 = 4ax. Its distance from the focus is minimum for the following value(s) of x.

Q10

If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is