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…

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 :

MARKS Content Team · Accepted Answer

Correct answer: (D) 4x+y+3=0. Equation of two parabola are y^2=3x and x^2=3y. Let equation of tangent to y^2=3x is y=mx+3/4m is also tangent to x^2=3y ⇒ x^2=3mx+9/4m ⇒4mx^2-12m^2x-9=0 have equal roots ⇒D=0 ⇒144m^4=44m(-9) ⇒m^4+m=0⇒m=-1 Hence, common tangent is y=-x-3/4 ⇒4x+y+3=0

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 :

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