MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Modulus Function

If y+3=m1x+...

Question

If $y + 3 = m_{1} (x + 2)$ and $y + 3 = m_{2} (x + 2)$ are two tangents to the parabola $y^{2} = 8 x$ , prove that $m_{1} m_{2} = - 1$ .

Open in App

Solution

Condition for tangents is c = a/m
so for first case $2 m_{1} - 3 = \frac{2}{m_{1}}$
and $2 m_{2} - 3 = \frac{2}{m_{2}}$
subtracting, $2 m_{1} - 3 - 2 m_{2} + 3 = \frac{2}{m_{1}} - \frac{2}{m_{2}}$
$2 (m_{1} - m_{2}) = 2 (\frac{1}{m_{1}} - \frac{1}{m_{2}})$
$\Rightarrow m_{1} - m_{2} = \frac{m_{2} - m_{1}}{m_{1} m_{2}}$
$\Rightarrow m_{1} - m_{2} = - \frac{m_{1} - m_{2}}{m_{1} m_{2}}$
$∴ m_{1} m_{2} = - 1$ Hence proved

Suggest Corrections

thumbs-up

0

Similar questions

y + 3 = m_{1} (x + 2)

y + 3 = m_{2} (x + 2)

are two tangents to the parabola

y^{2} = 8 x

y = m_{1} x + c

y = m_{2} x + c

are two tangents to the parabola

y^{2} + 4 a (x + a) = 0

y + b = m_{1} (x + a)

y - b = m_{2} (x + a)

are two tangents to the parabola

y^{2} = 4 a x

Q. If the lines

(y - b) = m_{1} (x + a)

(y - b) = m_{2} (x + a)

are two tangents to the parabola

y^{2} = 4 a x

Q. If the lines

(y - b) = m_{1} (x + a)

(y - b) = m_{2} (x + a)

are the tangents to the parabola

y^{2} = 4 a x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

The Moon Is Falling

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Modulus Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon