CameraIcon

SearchIcon

MyQuestionIcon

1

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

Chord of Contact

Points A and ...

Question

Points $A$ and $B$ lie on the parabola $y = 2 x^{2} + 4 x - 2$ , such that origin is the mid-point of the segment $A B$ . If $l$ is the length of the line segment $A B$ , then the value of $l^{2}$ is

Open in App

Solution

Given equation of the parabola
$y = 2 x^{2} + 4 x - 2$
Equation of the chord whose mid point is $(0, 0)$ will be
$T = S_{1} \Rightarrow 2 x \cdot 0 + 2 (x + 0) - 2 - \frac{(y + 0)}{2} = 2 (0)^{2} + 4 (0) - 2 - 0 \Rightarrow y = 4 x \dots (1)$
Now solving $(1)$ with the parabola equation
$4 x = 2 x^{2} + 4 x - 2 \Rightarrow x = \pm 1 ∴ y = \pm 4$
Hence $l = \sqrt{(4 + 4)^{2} + (1 + 1)^{2}}$
$∴ l^{2} = 68$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Points A and B lie on the parabola

y = 2 x^{2} + 4 x - 2

, such that origin is the mid-point of the line segment AB. If ‘l’ be the length of line segment AB, then find the unit digit of

l^{2}

A

B

lies on the parabola

y = 2 x^{2} + 4 x - 2

, such that origin is the mid-point of the segment

A B

l

is the length of the line segment

A B

, then the value of

l^{2}

Let A and B be two points on the parabola y=2x²+x-2 such that the origin is the midpoint of the line segment joining A to B. The length of AB is:

Let A and B be two points on the parabola $y = 2 x^{2} + x - 2$ such that the origin is the midpoint of the line segment joining $A$ to $B$ . The length of $A B$ is:

Q. If C is a point on the line segment AB of length 12 cm, such that AC =

\frac{2}{3}

of AB, then the value of

\frac{C B}{A B}

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Chord of Contact

Standard XIII Mathematics

Join BYJU'S Learning Program

CrossIcon