- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
normal
રેખા $ ℓx + my + n = 0$ એ અતિવલય $\frac{{{x^2}}}{{{a^2}}}\, - \,\,\frac{{{y^2}}}{{{b^2}}}\,\, = \,\,1$ નો સ્પર્શક ક્યારે કહેવાય ?
A
$a^2ℓ^2 - b^2m^2 = n^2$
B
$a^2 ℓ 2 + m^2 = n^2b^2$
C
$a^2 + b^2 = n^2(ℓ 2 + m^2)$
D
$a^2 ℓ 2 + b2m_2 = n2$
Solution
રેખા $y\,\, = \,\,mx\,\, + \;\,c\,\,\,$ એઅતિવલય $\,\frac{{{x^2}}}{{{a^2}}}\,\, – \,\,\frac{{{y^2}}}{{{b^2}}}\,\, = \,\,1$ નો સ્પર્શક તો જ હોય
જો ${c^2}\,\, = \,\,{a^2}{m^2}\,\, – \,\,{b^2}$
અહી $\,C\,\, = \,\, – \,\,\frac{n}{m}\,\,$ અને $m\,\, = \,\, – \frac{{l}}{m}$
( રેખા ${l}x\,\, + \;\,my\,\, + \;\,n\,\, = \,\,0$ માટે)
$ \Rightarrow \,\,\frac{{{n^2}}}{{{m^2}}}\,\, = \,\,{a^2}\,\frac{{l}}{{{m^2}}}\,\, – \,\,{b^2}\,\, \Rightarrow \,\,{n^2}\,\, = \,\,{a^2}\,{{l}^2}\,\, – \,\,{b^2}{m^2}$
Standard 11
Mathematics
Similar Questions
medium
