The locus of the point of intersection of two tangents of the ellipse $$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$$ which are inclined at angles $${{\theta }_{1}}$$, and $${{\theta }_{2}}$$ with the major axis such that $${{\tan }^{2}}{{\theta }_{1}}+{{\tan }^{2}}{{\theta }_{2}}$$ is constant, is

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TuteeHUB · Accepted Answer

$$4{{x}^{2}}{{y}^{2}}-2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}+{{a}^{2}})}^{2}}$$

TuteeHUB · Answer

$$4{{x}^{2}}{{y}^{2}}+2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}-{{a}^{2}})}^{2}}$$

TuteeHUB · Answer

$$4{{x}^{2}}{{y}^{2}}-2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}-{{a}^{2}})}^{2}}$$

TuteeHUB · Answer

None of these

1.	The locus of the point of intersection of two tangents of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] which are inclined at angles \[{{\theta }_{1}}\], and \[{{\theta }_{2}}\] with the major axis such that \[{{\tan }^{2}}{{\theta }_{1}}+{{\tan }^{2}}{{\theta }_{2}}\] is constant, is
A.	\[4{{x}^{2}}{{y}^{2}}+2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}-{{a}^{2}})}^{2}}\]
B.	\[4{{x}^{2}}{{y}^{2}}-2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}-{{a}^{2}})}^{2}}\]
C.	\[4{{x}^{2}}{{y}^{2}}-2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}+{{a}^{2}})}^{2}}\]
D.	None of these
Answer» C. \[4{{x}^{2}}{{y}^{2}}-2({{x}^{2}}-{{a}^{2}})({{y}^{2}}-{{b}^{2}})=k{{({{x}^{2}}+{{a}^{2}})}^{2}}\]

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