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10-2. Parabola, Ellipse, Hyperbola
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જો $\frac{x}{a}\,\, + \;\,\frac{y}{b}\,\, = \,\,\sqrt 2 $ ઉપવલય $\frac{{{x^2}}}{{{a^2}}}\,\, + \;\,\frac{{{y^2}}}{{{b^2}}}\,\, = \,\,1\,$ ને સ્પર્શે, તો તેનો ઉત્કેન્દ્રીકોણ (Eccentric Angle) $\,\theta \,\, = \,\, ............ $ $^o$
A
$0$
B
$90$
C
$45$
D
$60$
Solution
Equation of tangent in parametric form to an ellipse is $\frac{x \cos \theta}{a}+\frac{y \sin \theta}{b}=1$
Comparing it with given equation
$\Rightarrow \cos \theta=\frac{1}{\sqrt{2}}, \sin \theta=\frac{1}{\sqrt{2}}$
$\Rightarrow \theta=\frac{\pi}{4}$
So the eccentric angle is $45^{\circ}$
Standard 11
Mathematics
