If the line x-2y=12 is a tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the point 3,-9/2, then the length of the latus rectum of the ellipse is

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MARKS Content Team · Accepted Answer

Correct answer: (C) 9 units. ∵3,-9/2 lies on (x^2)/(a^2)+(y^2)/(b^2)=1⇒9/(a^2)+81/(4b^2)=1 ……(1) Equation of the tangent at 3,-9/2 is 3x/(a^2)+(-9)/2yb^2=1 & given equation of the tangent is: x-2y=12 ⇒x/12+ (-y)/6=1 On comparing these equations: (a^2)/3=12⇒a^2=36⇒a=6 (2b^2)/9=6⇒b^2=27⇒b=3√3 ∴Length of L.R.=(2b^2)/a=(2×27)/6=9

If the line $x - 2 y = 12$ is a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at the point $(3, - \frac{9}{2})$ , then the length of the latus rectum of the ellipse is

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More Ellipse Questions

If the line x-2y=12 is a tangent to the ellipse x2a2+y2b2=1 at the point 3,-92, then the length of the latus rectum of the ellipse is

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More Ellipse Questions

If the line $x - 2 y = 12$ is a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at the point $(3, - \frac{9}{2})$ , then the length of the latus rectum of the ellipse is