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find the common tangent to a circle x^2+y^2=2a^2 and the parabola y^2=8ax please reply soon!!!

find the common tangent to a circle x^2+y^2=2a^2 and the parabola y^2=8ax please reply soon!!!

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Equation of tangent to the parabola in slope form:
y = mx + \frac{2a}{m}…..............(1)
Equation of tangent to the circle in slope form:
y = mx + \sqrt{2}a\sqrt{1+m^{2}}…................(2)
Equation (1), (2) must be same
\frac{2a}{m} = \sqrt{2}a\sqrt{1+m^{2}}
m^{4}+m^{2}-2=0
(m^{2}+2)(m^{2}-1)=0
m = \pm 1
Equation of common tangents:
y = x+2a
y = -x-2a
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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