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10-2. Parabola, Ellipse, Hyperbola
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રેખા $y = \alpha x + \beta $ એ અતિવલય $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ નો સ્પર્શક હોય તો ચલિતબિંદુ $P(\alpha ,\,\beta )$ નો બિંદુગણ મેળવો.
A
પરવલય
B
અતિવલય
C
ઉપવલય
D
વર્તૂળ
(AIEEE-2005)
Solution
(b) If $y = mx + c$ is tangent to the hyperbola then ${c^2} = {a^2}{m^2} – {b^2}$.
Here ${\beta ^2} = {a^2}{\alpha ^2} – {b^2}$.
Hence locus of $P$($\alpha$, $\beta$) is ${a^2}{x^2} – {y^2} = {b^2}$,
which is a hyperbola.
Standard 11
Mathematics
