Equation of tangent of slope m to ellipse x2a2-y2b2-1 is y-mx-a2m2-b2

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Standard XII

Mathematics

Tangent to an Ellipse: Slope Form

Equation of t...

Question

Equation of tangent of slope $m$ to ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is
$y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$

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Similar questions

Q. What is the equation of the normal with slope m to the ellipse

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

The equation of tangent with slope $m$ to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is given by $y = m x \mp \sqrt{a^{2} + b^{2} m^{2}} .$

Q. The equation

y = m x + c

is a tangent to the

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

.Then show that

c^{2} = a^{2} m^{2} + b^{2}

What is the point of contact between the hyperbola
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ and
the tangent $y = m x \pm \sqrt{a^{2} m^{2} - b^{2}}$ .

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Equation of tangent of slope m to ellipse x2a2+y2b2=1 is y=mx±√a2m2+b2

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Equation of tangent of slope $m$ to ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is
$y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$