Statement 1: An equation of a common tangent to the parabola y2=163xand the ellipse 2x2+y2=4isy=2x+23.Statement 2: If the line y=mx+m43,(m=0)is a common tangent to the parabola y2=163xand the ellipse 2x2+y2=4, then m satisfies m4+2m2=24.

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Statement 1: An equation of a common tangent to the parabola {

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Statement 1: An equation of a common tangent to the parabola $y^{2} = 163 x$ and the ellipse $2 x^{2} + y^{2} = 4 i s y = 2 x + 23$ .Statement 2: If the line $y = m x + \frac{4 3}{m}, (m \neq = 0)$ is a common tangent to the parabola $y^{2} = 163 x$ and the ellipse $2 x^{2} + y^{2} = 4$ , then m satisfies $m^{4} + 2 m^{2} = 24$ .

Statement 1 is false, statement 2 is true

(3)x

and t h e e l l i p s e

2x^2+""y^2=""4""i s""y""=""2x""+""2sqrt(3)

. S t a t e m e n t 2 : I f t h e l \in e

y""=""m x""+(4sqrt(3))/m ,(m!=0)

i s a c o m m o n tan \geq n t \to t h e p a r a b o l a

y^2=""16sqrt(3)x

and t h e e l l i p s e

2x^2+""y^2=""4

, t h e n m s a t i i e s

m^4+""2m^2=""24

. (1) S t a t e m e n t 1 i s f a l s e, s t a t e m e n t 2 i s t r u e (2) ∣ ∣ x

and the ellipse

2 x^{2} + y^{2} = 4 i s y = 2 x + 23

.Statement 2: If the line

y = m x + \frac{4 3}{m}, (m \neq = 0)

is a common tangent to the parabola

y^{2} = 163 x

and the ellipse

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

, then m satisfies

m^{4} + 2 m^{2} = 24

.(1) Statement 1 is false, statement 2 is true(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

Statement 1 is true, statement 2 is false

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Alexander Discussed

Statement 1: An equation of a common tangent to the parabola

y^{2} = 163 x

and the ellipse

2 x^{2} + y^{2} = 4 i s y = 2 x + 23

.Statement 2: If the line

y = m x + \frac{4 3}{m}, (m \neq = 0)

is a common tangent to the parabola

y^{2} = 163 x

and the ellipse

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

, then m satisfies

m^{4} + 2 m^{2} = 24

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Question Text	Statement 1: An equation of a common tangent to the parabola $y^{2} = 163 x$ and the ellipse $2 x^{2} + y^{2} = 4 i s y = 2 x + 23$ .Statement 2: If the line $y = m x + \frac{4 3}{m}, (m \neq = 0)$ is a common tangent to the parabola $y^{2} = 163 x$ and the ellipse $2 x^{2} + y^{2} = 4$ , then m satisfies $m^{4} + 2 m^{2} = 24$ .
Answer Type	Video solution: 1
Upvotes	150

Statement 1: An equation of a common tangent to the parabola y2=163​xand the ellipse 2x2+y2=4isy=2x+23​.Statement 2: If the line y=mx+m43​​,(m=0)is a common tangent to the parabola y2=163​xand the ellipse 2x2+y2=4, then m satisfies m4+2m2=24.

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