Question

two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is

Answer 1

Length of the latus rectum = 4a

For the parabola

y² = 4ax

Equation of tangent -

y = mx + a/m

Tangent to y² = 4ax is slope form.

Common tangent of x² = 3y and y² = 3x

y = mx - 3/4 m²

y = mx + 3/4m

on solving 3/4m² = 3/4m = 1

m = -1

We get

x + y + 3/4 = 0

= 4 (x + y) + 3 = 0

Option 1:

3 (x+y) + 3 = 0