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Prove that the least focal chord of a pa...

Prove that the least focal chord of a parabolaa is it rectum.

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Prove that the least focal chord of a parabola is its latus rectum .

Prove that the least focal chord of a parabola is the latus rectum .

Prove that the normal at the extermities of a focal chord of a parabola intersect at right angles.

Show that the circle described on a focal chord of a parabola as diameter touches its directrix .

Prove that "The greatest chord of circle is its diameter".

Prove that the sum of the reciprocals of the segments of any focal chord of a parabola is constant .

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

Find the locus of the point of intersection of the normals at the end of the focal chord of the parabola y^2=4a xdot

Show that the sum of the reciprocals of the segments of any focal chord of a parabola y^2=4ax is constant.

Prove that the lengths of the chord of a circle which subtends an angle 108^(@) at the centre is equal to the sum of the lenths of the chords which subtend angles 36^(@) and 60^(@) at the centre of the same circle.

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 14-EXERCISE
  1. How many arragements can be made out of the letters of the word FAILUR...

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  2. Calcualte the sum of the series :1+3/2+7/4+15/8+31/16+….+tn

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  3. The equation of three sides of a triangle are x + 2y - 5 = 0, x +y = 6...

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  4. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  5. Find the equation, centre, and radius of a circle which is passes thro...

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  6. By using section formula, show that the points .(1, 2, 3), (-2, 4, 2) ...

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  7. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

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  8. If f(x)=sqrt2x-sqrt(2/x)+(4-x)/(4-x), find the value of f(2)

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  9. If 2x^3 + 5x = 0, where x is a real number, then x = 0’ examine the st...

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  10. ‘If for any real no x, x^3 + x = 0, then x =0’ prove this by the metho...

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  11. A,B,C and D are four mutually exclusive and exhuastive events. If the ...

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  12. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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  13. Prove that tan 70^@ = tan 20^@ + 2 tan 50^@.

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  14. Prove that with the help of mathemetical induction. 4+44+444+...upto n...

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  15. If the roots of the equation ax^2+bx+c=0 are alpha,betaand the roots ...

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  16. Draw the graph and find the common region of the following system of i...

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  17. Show that there are 136 ways of selecting 4 letters from the word EXAM...

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  18. Prove that the least focal chord of a parabolaa is it rectum.

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  19. Find the eccentricity and the equation of directix of the ellipse x^2/...

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  20. Show that the difference of the focal distances of any point on the hy...

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