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If any tangent to the ellipse x^(2)/a^(2...

If any tangent to the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` cuts off intercepts of length h and k on the axes, then `a^(2)/h^(2)+b^(2)/k^(2)`is equal to

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If any tangent to the ellipse x^2/a^2+y^2/b^2=1 cuts off intercepts of length h and k on the axes, then a^2/h^2+b^2/k^2= (A) 0 (B) 1 (C) -1 (D) Non of these

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

Area of ellipse x^2/a^2 + y^2/b^2 = 1, a > b is :

Tangents at right angle are drawn to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 . Show that the focus of the middle points of the chord of contact is the curve (x^(2)/a^(2)+y^(2)/b^(2))^(2)=(x^(2)+y^(2))/(a^(2)+b^(2)) .

Find the eccentricity of the ellipse x^(2)/(a^(2))+y^(2)/b^(2)=1 when a=5 and b=3.

The equations of the tangents to the ellipse 3x^(2)+y^(2)=3 making equal intercepts on the axes are

Write the equation of tangent to the ellipse (x^2)/(25)+(y^2)/(16)=1 at any point P .

The parametric angle alpha where -piltalphalepi of the point on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 at which the tangent drawn cuts the intercept of minimum length on the coordinates axes, is/are

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Find the focus of the parabola x^2=4y

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  2. Show that the locus of the middle points of normal chords of the parab...

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  3. If any tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cuts off inter...

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  4. The vertices of a quadrilateral are situated at foci and the extremiti...

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  5. Find the equation of the hyperbola whose foci are (8, 3), (0, 3) and w...

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  6. Find the slope of the line passing through the points : (3, - 2) and...

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  7. The slope of the line passing through the points (3,-2) and (-1,4) is:

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  8. Slope of the line passing through the points (3, -2) and (3, 4) is:

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  9. If the equation of a circle is: x^2 + y^2 + 8x -10y+8=0, then its cent...

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  10. The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

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  11. If the equation of a circle is: x^2 + y^2-4x-8y -45 =0, then its centr...

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  12. The centre of the circle x^2+y^2+8x+10y-8=0 is:

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  13. The radius of the circle : x^2 + y^2-8x + 10y- 12 =0 is:

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  14. The directrix of the parabola y^2=4ax is :

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  15. The directrix of the parabola y^(2) + 4x + 3 = 0 is :

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  16. The focus of the parabola y^2= 4ax is :

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  17. The vertex of the parabola y^2= 4ax is

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  18. The focus of the parabola y = 2x^2 + x is

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  19. The foci of the ellipse 9x^2 +4y^2 =36 are

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  20. The eccentricity of the parabola y^2 =-8x is :

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