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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
The smallest possible positive slope of a line whose $y$-intercept is $5$ and which has a common point with the ellipse $9 x^2+16 y^2=144$ is
  • A
    $\frac{3}{4}$
  • ✓
    $1$
  • C
    $\frac{4}{3}$
  • D
    $\frac{9}{16}$
✓

Answer

Correct option: B.
$1$
b
(b)

We have equation of ellipse

$9 x^2+16 y^2 =144$

$\Rightarrow \quad \frac{x^2}{16}+\frac{y^2}{9} =1$

Equation of tangent of ellipse is

$y =m x \pm \sqrt{a^2 m^2+b^2}$

$\therefore \quad y =m x \pm \sqrt{16 m^2+9}$

Now, given $y$-intercept $=5$

$\therefore \sqrt{16 m^2+9}=5 \Rightarrow 16 m^2+9=25$

$\Rightarrow \quad 16 m^2=16 \Rightarrow m=\pm 1$

$\therefore \text { Positive slope }=1$

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