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10-2. Parabola, Ellipse, Hyperbola
easy
શાંકવ $\frac{{{x^2}}}{{{a^2}}}\,\, + \;\,\frac{{{y^2}}}{{{b^2}}}\,\, = \,\,1\,\,$ ને રેખા $x\cos \alpha \,\, + \,y\sin \,\alpha \,\, = \,p\,\,$ ક્યારે સ્પર્શશે?
A
$p^2 = a^2 sin^2\alpha + b^2 cos^2\ \alpha$
B
$p^2 = a^2 + b^2$
C
$p^2 = b^2sin^2\alpha + a^2cos^2\alpha$
D
એકપણ નહિ
Solution
જો $\frac{{\text{p}}}{{{\text{sin}}\,\,\alpha }}\,\, = \,\, \pm \,\,\sqrt {{b^2}\,\, + \;\,{a^2}\,{{\cot }^2}\,\,\alpha } $
અથવા ${p^2}\,\, = \,\,{b^2}\,\,{\sin ^2}\,\alpha \,\, + \;\,{a^2}{\cos ^2}\,\,\alpha $ હોય તો
$\frac{{{x^2}}}{{{a^2}}}\,\, + \;\,\frac{{{y^2}}}{{{b^2}}}\,\, = \,\,1\,$
નો સ્પર્શક $\,y\,\, = \,\, – x\cot \alpha \,\, + \;\,\frac{p}{{\sin \,\,\alpha }}$ હોય
Standard 11
Mathematics
