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The line x cos alpha + y sin alpha +y...

The line x cos `alpha + y sin alpha +y sin alpha =p` is tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1.`if

A

`a^2 cos^2 alpha + b^2 sin^2 alpha = p^2`

B

`a^2 sin^2 alpha + b^2 cos^2 alpha = p^2`

C

`a^2 cos^2 alpha - b^2 sin^2 alpha = p^2`

D

`a^2 sin^2 alpha - b^2 cos^2 alpha = p^2`

Text Solution

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The correct Answer is:
A
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ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
  1. Tangents are drawn to the ellipse (x^2)/(9) + (y^2)/(5) = 1 at end of ...

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  2. From a point on the axis of x common tangents are drawn to the parabol...

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  3. The line x cos alpha + y sin alpha +y sin alpha =p is tangent to ...

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  4. If a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 makes eq...

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  5. An ellipse passes through the point (4,-1) and touches the line x+4...

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  6. If a tangent having a slope of -4/3 to the ellipse x^2/18 + y^2/32 = 1...

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  7. The sum of the squares of the perpendiculars on any tangents to the ...

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  8. The product of the perpendiculars drawn from the two foci of an ellips...

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  9. The points (1, -1) and (2, - 1) are the foci of an ellipse and the lin...

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  10. If F1 and F2 be the feet of the perpendiculars from the foci S1 and S2...

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  11. if the tangent at the point (4 cos phi , (16)/(sqrt(11) )sin phi ...

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  12. The length of a common tangent to x^2 + y^2 = 16 and 9x^2 + 25y^2 = 22...

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  13. If x/a + y/b = sqrt(2) touches the ellipse (x^2)/(a^2) + (y^2)/(b^2) =...

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  14. If sqrt(3) bx +ay = 2ab touches the ellipse (x^2)/(a^2) + (y^2)/(b^2) ...

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  15. The eccentric angle of a point P lying in the first quadrant on the el...

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  16. If theta is the angle between the pair of tangents drawn to the ellips...

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  17. Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=...

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  18. An ellipse slides between two perpendicular lines the locus of ...

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  19. The line 2x+y=3 cuts the ellipse 4x^(2)+y^(2)=5 at points P and Q. If ...

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  20. If the normal at one end of the latus rectum of the ellipse (x^2)/(...

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