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

Byju's Answer

Standard XII

Mathematics

Chord of Contact

Points A and ...

Question

Points $A$ and $B$ lies 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

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}

.___

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 segment

A B

. If

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}

will be .

Join BYJU'S Learning Program

Explore more

Chord of Contact

Standard XII Mathematics

Join BYJU'S Learning Program

Points A and B lies on the parabola y=2x2+4x−2, such that origin is the mid-point of the segment AB. If l is the length of the line segment AB, then the value of l2 is

Given equation of the parabola y=2x2+4x−2 Equation of the chord whose mid point is (0,0) will be T=S1⇒2x⋅0+2(x+0)−2−(y+0)2=2(0)2+4(0)−2−0⇒y=4x⋯(1) Now solving (1) with the parabola equation 4x=2x2+4x−2⇒x=±1∴y=±4 Hence l=√(4+4)2+(1+1)2∴l2=68

Points $A$ and $B$ lies 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