You visited us 6 times! Enjoying our articles? Unlock Full Access!

Four Common Forms of Parabola Equation

The line 2x...

Question

The line $2 x + 3 y + 9 = 0$ touches the parabola $y^{2} = 8 x$ at the point

(0, - 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(2, 4)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(- 6, \frac{9}{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{9}{2}, - 6)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $(\frac{9}{2}, - 6)$
Given lines and parabola are $2 x + 3 y + 9 = 0$ and $y^{2} = 8 x$ respectively
To get the point of intersection, solve both the curves
$y^{2} = 4 (2 x) = 4 (- 3 y - 9)$ , use line equation
$\Rightarrow y^{2} + 12 y + 36 = 0$
$\Rightarrow (y + 6)^{2} = 0$
$\Rightarrow y = - 6$
Thus $x = - \frac{1}{2} (3 y + 9) = - \frac{1}{2} (- 18 + 9) = \frac{9}{2}$

Hence the point of intersection is $(\frac{9}{2}, - 6)$

Suggest Corrections

Similar questions

I . x^{2} + y^{2} = 1

a

) (0, 0)

x^{2} + y^{2} - 2 x = 1

x^{2} + y^{2} - 2 y = 1

I I . x^{2} + y^{2} - x + 3 y - 3 = 0, b) (2, 3)

x^{2} + y^{2} - 2 x + 2 y + 2 = 0

x^{2} + y^{2} + 2 x + 3 y - 9 = 0

I I I . x^{2} + y^{2} - 8 x + 40 = 0, c) (8, - 15 / 2)

x^{2} + y^{2} - 5 x + 16 = 0

x^{2} + y^{2} - 8 x + 16 y + 160 = 0

P

x^{2} + y^{2} + x - 3 = 0, 3 x^{2} + 3 y^{2} - 5 x + 3 y = 0

4 x^{2} + 4 y^{2} + 8 x + 7 y + 9 = 0

P

x + y = 5

(6, - 1)

y^{2} = 8 x

45^{\circ}

2 x + y + 3 = 0

x^{2} + y^{2} - x + 3 y - 3 = 0

x^{2} + y^{2} - 2 x + 2 y + 2 = 0

x^{2} + y^{2} + 2 x + 3 y - 9 = 0

x - 3 y + k = 0

3 y^{2} = 4 x

k = 5

y^{2} = 8 x

30^{0}

x - \sqrt{3} y + 6 = 0

Join BYJU'S Learning Program