HyperbolaHard
Question
The equation of the common tangent to the parabola y2 = 8x and the hyperbola 3x2 - y2 = 3 is -
Options
A.2x ± y + 1 = 0
B.x ± y + 1 = 0
C.x ± 2y + 1 = 0
D.x ± y + 2 = 0
Solution
Let the slope of common tangent be m.
Equation of tangent to parabola is
y = mx + 2/m ....(i)
Equation of tangent to hyperbola is
y = mx ±
... (ii)
By comparing (i) & (ii), we get m = ± 2.
∴ Equation of common tangent is y = ± (2x + 1)
i.e. 2x ± y + 1 = 0.
Equation of tangent to parabola is
y = mx + 2/m ....(i)
Equation of tangent to hyperbola is
y = mx ±
... (ii)By comparing (i) & (ii), we get m = ± 2.
∴ Equation of common tangent is y = ± (2x + 1)
i.e. 2x ± y + 1 = 0.
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