- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
normal
Slope of common tangents of parabola $(x -1)^2 = 4(y -2)$ and ellipse ${\left( {x - 1} \right)^2} + \frac{{{{\left( {y - 2} \right)}^2}}}{2} = 1$ are $m_1$ and $m_2$ ,then $m_1^2 + m_2^2$ is equal to
A
$2$
B
$3$
C
$4$
D
$6$
Solution
$\mathrm{X}^{2}=4 \mathrm{Y}, \mathrm{X}^{2}+\frac{\mathrm{Y}^{2}}{2}=1$
$\mathrm{y}=\mathrm{mx}-\mathrm{m}^{2}$
$y=m x-\sqrt{m^{2}+2}$
$\mathrm{m}^{2}=\sqrt{\mathrm{m}^{2}+2}$
$\Rightarrow m^{4}-m^{2}-2=0$
$\mathrm{m}^{2}=2,-1 \Rightarrow \mathrm{m}$
$\mathrm{m}_{1}^{2}+\mathrm{m}_{2}^{2}=4$
Standard 11
Mathematics
