Two parabolas with a common vertex and with axes along the 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

Question

Two parabolas with a common vertex and with axes along the 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 :

TestHub · Accepted Answer

Equation of two parabola are y 2 = 3 x and x 2 = 3 y . Let equation of tangent to y 2 = 3 x is y = m x + 3 4 m is also tangent to x 2 = 3 y ⇒ x 2 = 3 m x + 9 4 m ⇒ 4 m x 2 - 12 m 2 x - 9 = 0 have equal roots ⇒ D = 0 ⇒ 144 m 4 = 4 4 m ( - 9 ) ⇒ m 4 + m = 0 ⇒ m = - 1 Hence, common tangent is y = - x - 3 4 ⇒ 4 x + y + 3 = 0

Mathematics - Parabola Question with Solution | TestHub

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