Question
If 2y = x + 24 is a tangent to parabola y^{2} = 24x, then its distance from parallel normal is

1



easy
Solution
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
Find the locus of the midpoint of the chords of the parabola y^{2} = 4ax which subtend a right angle at the vertex of the parabola.
Show that the normal at a point (at^{2}, 2at) on the parabola y^{2} = 2ax cuts the curve again at the point whose parameter .
Show that the normal at a point (at^{2}, 2at) on the parabola y^{2} = 2ax cuts the curve again at the point whose parameter .
Find the locus of a pint P which moves such that two of the three normal’s drawn from it to the parabola y^{2} = 4ax are mutually perpendicular.
If normal at the point (at^{2}, 2at) in the parabola y^{2} = 4axintersects the parabola again at the (am^{2}, 2am), then find the minimum value of m^{2}.
The equation of circle touching the parabola y^{2} = 4x at the point (1, –2) and passing through origin is
The vertex of a parabola is the point (a, b) and latusrectum is of length l. If the axis of the parabola is along the positive direction of yaxis. Then its equation is
Slope of common tangent to parabolas y^{2} = 4x and x^{2} = 8y is
If a focal chord with positive slope of the parabola y^{2} = 16xtouches the circle x^{2} + y^{2} – 12x + 34 = 0, then m is
PQ is a focal chord of the parabola y^{2} = 4ax, O is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.