## Question

### Solution

#### SIMILAR QUESTIONS

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

If the line 2*x* + 3*y* = 1 touch the parabola *y*^{2} = 4*ax* at the point*P*. Find the focal distance of the point *P*.

Find the angle between the tangents of the parabola *y*^{2} = 8*x*, which are drawn from the point (2, 5).

Find the locus of middle point of chord *y*^{2} = 4*ax* drawn through vertex.

Find the locus of the mid-point of the chords of the parabola *y*^{2} = 4*ax* which subtend a right angle at the vertex of the parabola.

Show that the normal at a point (*at*^{2}, 2*at*) on the parabola *y*^{2} = 2*ax* cuts the curve again at the point whose parameter .

Show that the normal at a point (*at*^{2}, 2*at*) on the parabola *y*^{2} = 2*ax* 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} = 4*ax* are mutually perpendicular.

If normal at the point (*at*^{2}, 2*at*) in the parabola *y*^{2} = 4*ax*intersects the parabola again at the (*am*^{2}, 2*am*), then find the minimum value of *m*^{2}.

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