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Question: The area of the quadrilateral formed by the tangents at the end points of the latus rectum to the el...

The area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse x29+y25=1\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1, is

Explanation

Solution

We know that the ends of latus rectum of an ellipse x2a2+y2b2=1\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1 are (±ae,b2a)\left( \pm ae,\dfrac{{{b}^{2}}}{a} \right). We know that tangent of ellipse x2a2+y2b2=1\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1 at (x1,y1)\left( {{x}_{1}},{{y}_{1}} \right) is xx1a2+yy1b2=1\dfrac{x{{x}_{1}}}{{{a}^{2}}}+\dfrac{y{{y}_{1}}}{{{b}^{2}}}=1. We know that there will be four latus rectums for an ellipse. So, the area of a quadrilateral ellipse formed by all the latus rectums is equal to 4 times of the area of the triangle formed by a single latus rectum. So, we can find the area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse x29+y25=1\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1

Complete step-by-step answer:
We know that the eccentricity of ellipse x2a2+y2b2=1\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1 is equal to 1b2a2\sqrt{1-\dfrac{{{b}^{2}}}{{{a}^{2}}}}.
Now we should find the eccentricity of x29+y25=1\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1.
Let us compare x2a2+y2b2=1\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1 with x29+y25=1\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1.
Then we get

& {{a}^{2}}=9.....(1) \\\ & {{b}^{2}}=5.....(2) \\\ \end{aligned}$$ Let us the eccentricity of $$\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1$$ is equal to e. $$\Rightarrow e=\sqrt{1-\dfrac{{{b}^{2}}}{{{a}^{2}}}}.....(3)$$ Now, let us substitute equation (1) and equation (2) in equation (3), then we get $$\begin{aligned} & \Rightarrow e=\sqrt{1-\dfrac{5}{9}} \\\ & \Rightarrow e=\sqrt{\dfrac{9-5}{9}} \\\ & \Rightarrow e=\sqrt{\dfrac{4}{9}} \\\ & \Rightarrow e=\dfrac{2}{3}.....(4) \\\ \end{aligned}$$ 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) We know that the ends of latus rectum of an ellipse $$\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1$$ are $$\left( \pm ae,\dfrac{{{b}^{2}}}{a} \right)$$. Now we should find the value of $$ae$$. From equation (1) and equation (4), we get $$\begin{aligned} & \Rightarrow ae=\left( 3 \right)\left( \dfrac{2}{3} \right) \\\ & \Rightarrow ae=2....(5) \\\ \end{aligned}$$ Now we should find the value of $$\dfrac{{{b}^{2}}}{a}$$. $$\Rightarrow \dfrac{{{b}^{2}}}{a}=\dfrac{5}{3}..(6)$$ From equation (5) and equation (6), we get that the ends of the latus rectum are $$\left( \pm 2,\dfrac{5}{3} \right)$$. Now let us find the tangent equation of $$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1$$ with $$\left( 2,\dfrac{5}{3} \right)$$. We know that tangent of ellipse $$\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1$$ at $$\left( {{x}_{1}},{{y}_{1}} \right)$$ is $$\dfrac{x{{x}_{1}}}{{{a}^{2}}}+\dfrac{y{{y}_{1}}}{{{b}^{2}}}=1$$. So, the equation of tangent equation of $$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1$$ with $$\left( 2,\dfrac{5}{3} \right)$$ is $$\Rightarrow \dfrac{2x}{9}+\dfrac{\left( \dfrac{5}{3} \right)y}{5}=1$$ $$\Rightarrow \dfrac{2x}{9}+\dfrac{y}{3}=1......(7)$$ From equation (7), it is clear that $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$ is the tangent equation of $$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1$$ at $$\left( 2,\dfrac{5}{3} \right)$$. Now, we should find the area of the quadrilateral of $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$ with respect to axes. Now, we should find the point where $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$ meet the x-axis. So, let us substitute the value of y is equal to 0 in $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$. $$\begin{aligned} & \Rightarrow \dfrac{2x}{9}+\dfrac{y}{3}=1 \\\ & \Rightarrow \dfrac{2x}{9}=1 \\\ \end{aligned}$$ $$\Rightarrow x=\dfrac{9}{2}.....(8)$$ Now, we should find the point where $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$ meet the y-axis. So, let us substitute the value of x is equal to 0 in $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$. $$\begin{aligned} & \Rightarrow \dfrac{2x}{9}+\dfrac{y}{3}=1 \\\ & \Rightarrow \dfrac{y}{3}=1 \\\ \end{aligned}$$ $$\Rightarrow y=3.....(9)$$ So, it is clear that $$\dfrac{2x}{9}+\dfrac{y}{3}=1$$ meets x-axis at $$A\left( \dfrac{9}{2},0 \right)$$ and y-axis at $$B\left( 0,3 \right)$$. We know that area of the triangle is equal to half of the product of OA and OB. So, the area of the triangle OAB is equal to half of the product of OA and OB. $$\begin{aligned} & \Rightarrow \text{Area of }\Delta \text{OAB=}\dfrac{1}{2}\left( OA \right)\left( OB \right) \\\ & \Rightarrow \text{Area of }\Delta \text{OAB=}\dfrac{1}{2}\left( \dfrac{9}{2} \right)\left( 3 \right) \\\ & \Rightarrow \text{Area of }\Delta \text{OAB=}\dfrac{27}{4}......(10) \\\ \end{aligned}$$ From equation (1), it is clear that the area of the triangle formed by a latus rectum is equal to $$\dfrac{27}{4}$$. We know that there will be four latus rectums for an ellipse. So, the area of a quadrilateral ellipse formed by all the latus rectums is equal to 4 times of the area of the triangle formed by a single latus rectum. Let us assume the area of the quadrilateral is equal to A. $$\begin{aligned} & \Rightarrow A=4\left( \dfrac{27}{4} \right) \\\ & \Rightarrow A=27....(11) \\\ \end{aligned}$$ So, it is clear that the area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse $$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1$$ is 27. **Note:** Students have a misconception that the ends of latus rectum of an ellipse are equal to $$\left( \pm \dfrac{{{b}^{2}}}{a},ae \right)$$. If this misconception is followed, then we get an incorrect equation of latus rectum. Then we will get the incorrect are of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse $$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{5}=1$$. So, the misconception should be avoided.