Equation of two parabola are y2=3x and x2=3y.
Let equation of tangent to y2=3x is y=mx+4m3 is also tangent to x2=3y
⇒x2=3mx+4m9
⇒4mx2−12m2x−9=0 have equal roots
⇒D=0
⇒144m4=4(4m)(−9)
⇒m4+m=0⇒m=−1
Hence, common tangent is y=−x−43
⇒4(x+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 :
Held on 15 Apr 2018 · Verified 6 Jul 2026.
3(x+y)+4=0
8(2x+y)+3=0
x+2y+3=0
4(x+y)+3=0
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