Question

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Solution

Correct option is

Rewrite the tangent as 

So it is a tangent with the slope 

Now normal with same slope

        

Distance between these two parallel line will be .

SIMILAR QUESTIONS

Q1

Find the locus of the mid-point of the chords of the parabola y2 = 4ax which subtend a right angle at the vertex of the parabola.

Q2

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q3

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q4

Find the locus of a pint P which moves such that two of the three normal’s drawn from it to the parabola y2 = 4ax are mutually perpendicular.

Q5

If normal at the point (at2, 2at) in the parabola y2 = 4axintersects the parabola again at the (am2, 2am), then find the minimum value of m2.

Q6

The equation of circle touching the parabola y2 = 4x at the point  (1, –2) and passing through origin is

Q7

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

Q8

Slope of common tangent to parabolas y2 = 4x and x2 = 8y is

Q9

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is

Q10

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.