Question
The equation of the common tangents to the parabolas y2 = 4x and x2 = 32y is-
- x + 2y = 4
- x = 2y + 4
- x = 2y – 4
- x + 2y + 4 = 0
Hint:
find the equation of tangent to the first parabola and substitute the value of y or x in the other equation since they intersect at a point.
The correct answer is: x + 2y + 4 = 0
x = 2y – 4
equation of tangent to y2= 4ax : y= mx + 1/m
substituting the value of y in x2= -32y, we get
in x2= -32(mx+1/m) or
x2+32mx + 32/m=0
the above equation will have equal roots since the tangent touches the parabola at a point.
Therefore, D=0
On solving, we get 8m3-1=0 or m=1/2
Hence, y=x/2+2
2y=x+4
x-2y+4=0
the equation of tangent to the parabola y2= 4ax is y = mx + a/m
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