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If the parabolas y^2=4a x and y^2=4c(x-b...

If the parabolas `y^2=4a x` and `y^2=4c(x-b)` have a common normal other than the x-axis `(a , b , c` being distinct positive real numbers), then prove that `b/(a-c)> 2.`

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A DAS GUPTA-Integrated Tests-Exercise
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  2. Let C be any circle with centre ( 0, sqrt( 2)). Prove that at most two...

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  3. A discontinuous function y = f(x) satisfying x^2 + y^2= 4 is given b...

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  4. An ellipse has OB as a semi-minor axis, F and F' are its two foci and ...

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  5. A die is thrown three times and the sum of the 3 numbers shown is 15. ...

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  6. Fill in the blanks ine ach of the following so that that resulting sen...

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  7. The equation x e^(x) = 2 has

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  8. A function f(x)=x[1+(1/3) sin (Inx^2)], x != 0. integral part f(0)=0. ...

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  9. Prove that sum(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2,w h e r engeq3i sa nin...

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  10. ABC is an isosceles triangle inscribed in a circle of radius r , if AB...

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  11. Let z1 and z2 be the root of the equation z^2+pz+q=0 where the coeffic...

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  12. Let f(x) = {{:({1+|sin x|}^(a//|sin x|)", " pi/6 lt x lt 0),(" ...

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  13. Determine the constant c such that the straight line joining the point...

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  14. Two vertices of an equilateral triangle are (-1,0) and (1, 0), and its...

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  15. If x^2+px=q is an integer for every integral value of x then which is ...

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  16. If theta is the angle between the unit vectors hat a and hat b then co...

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  17. A bag A contains 2 white and 3 red balls and a bag B contains 4 white ...

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  18. If (1 + x + x^(2) + x^(3))^(n)= a(0) + a(1)x + a(2)x^(2) + a(3) x^(3) ...

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  19. If the parabolas y^2=4a x and y^2=4c(x-b) have a common normal other t...

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  20. A curve y=f(x) passes through the point P(1,1). The normal to the curv...

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