Slope of the common tangent to the ellipses x2-a2-b2-y2-b2-1- x2-a2-y2-a2-b2-1 is-

The correct option is B a/b Condition of common tangent will be c ^ 2 =( a ^ 2 + b ^ 2 ) #160; m ^ 2 + b ^ 2 = a ^ 2 m ^ 2 +( a ^ 2 + b ^ 2 ) ...

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Equation of Tangent at a Point (x,y) in Terms of f'(x)

Slope of the ...

Question

Slope of the common tangent to the ellipses $\frac{x^{2}}{a^{2} + b^{2}} + \frac{y^{2}}{b^{2}} = 1, \frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2} + b^{2}} = 1$ is:

\frac{2 a}{b}

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\frac{2 b}{a}

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\frac{a}{b}

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\frac{b}{a}

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Solution

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\frac{x^{2}}{a^{2} + b^{2}} + \frac{y^{2}}{b^{2}} = 1 & \frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2} + b^{2}} = 1

\frac{x^{2}}{a^{2} + b^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2} + b^{2}} = 1

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1

r (< a)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, (a > b)

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1

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