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If the line lx+my +n=0 touches the e...

If the line lx+my +n=0 touches the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` then

A

`a^(2)l^(2)+b^(2) m^(2)=n^(2)`

B

`a^(2)m^(2)+b^(2)l^(2)=n^(2)`

C

`a^(2)n^(2)+b^(2)m^(2)=l^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
the equation of the line is
`lx +my +n=0 if c^(2)=a^(2) m^(2)+b^(2)`
so line (i) will touch the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` if
` (-(n)/(m))^(2)=a^(2)(-(l)/(m))^(2)+b^(2) implies n^(2)=a^(2)l^(2)+b^(2)m^(2)`
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OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Chapter Test
  1. If the line lx+my +n=0 touches the ellipse (x^(2))/(a^(2))+(y^(2)...

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  2. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  3. A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&...

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  4. The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the cent...

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  5. If the minor axis of an ellipse subtends an angle of 60^(@) at each fo...

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  6. Let Sa n dS ' be two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . I...

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  7. The equation of the normal at the point P (2, 3) on the ellipse 9x^(2)...

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  8. For the ellipse 3x^(2) + 4y^(2) + 6x - 8y - 5 = 0 the eccentrically, i...

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  9. Let S, S' be the focil and BB' be the minor axis of the ellipse (x^(2)...

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  10. If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + ...

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  11. if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord t...

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  12. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  13. If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^...

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  14. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

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  15. The tangent at any point P on the ellipse meets the tangents at the ve...

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  16. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  17. The equation of the locus of the poles of normal chords of the ellipse...

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  18. The locus of mid-points of focal chords of the ellipse (x^2)/(a^2)+(y^...

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  19. The locus of a point whose polar with respect to the ellipse (x^2)/(a^...

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  20. if the chord of contact of tangents from a point P to the hyperbola x...

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  21. The locus of the poles of tangents to the auxiliary circle with respec...

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