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about to only mathematics

A

2

B

1

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
1,2,4
Any point on x+y=1 can be taken as (t,1-t).
The equation of chord with this as midpoint is
`y(1-t)-2a(x+t)=(1-t)^(2)-4at`
It passes through (a,2a). So,
`t^(2)-2t+2a^(2)-2a+1=0`
This should have two distinct real roots. So,
Discriminant `gt0i.e.,a^(2)-alt0`
`0ltaltor0lt4alt4`
So, length of latua rectum lies in (0,4)
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CENGAGE-PARABOLA-Exercise (Multiple)
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  6. The equation of the directrix of the parabola with vertex at the origi...

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  10. If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0...

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  11. The equation of the line that touches the curves y=x|x| and x^2+(y^2-2...

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  13. The line x+ y +2=0 is a tangent to a parabola at point A, intersect t...

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  14. Which of the following line can be normal to parabola y^2=12 x ? x+y-...

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  15. A normal drawn to the parabola =4a x meets the curve again at Q such t...

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  16. A circle is drawn having centre at C (0,2) and passing through focus ...

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  17. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

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