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Analytical Geometry> find the common tangent to a circle x^2+y...

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

John Doe , 11 Years ago

Grade 12th pass

2 Answers

Arun Kumar

Last Activity: 11 Years ago

Hello Student,

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
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

Yash Chourasiya

Last Activity: 4 Years ago

Dear Studnet

Let common tangent to the curves be

Now Distance from (0, 0) to the tangent line = Radius of circle

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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