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answer any two questions :(iii) if the straight line lx+my=n be a normal to the hyperbola `x^2/a^2 -y^2/b^2 =1`, then by the application of calculus prove that `a^2/l^2-b^2/m^2=(a^2+b^2)^2/n^2 `.

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If the straight line lx+my+n=0 be a normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then by the application of calculus, prove that (a^2)/(l^2)-(b^2)/(m^2)=((a^2+b^2)^2)/(n^2) .

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UNITED BOOK HOUSE-SET 12-EXERCISE
  1. Find the intercept form of a plane with intercepts 2,3 and 4 on the x,...

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  2. A and B are two independent events with P(A) = 2/5 and P(B) = 1/3, eva...

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  3. The mean and variance of a binomial distribution are 4 and 3 respectiv...

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  4. If tan^(-1)x, tan^(-1)y and tan^(-1)z are in A.P, find the algebric re...

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  5. Prove that, the inverse of a given square matrix, if its exists, is un...

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  6. Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

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  7. If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfra...

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  8. Evaluate: int (xdx)/[(x^2 - a^2)(b^2-x^2)] (b^2>a^2).

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  9. Evaluate: int(sqrt x dx)/sqrt(a^3 - x^3)

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  10. Solve:(dy)/(dx)-y/x + cosec (y/x)=0, given y = 0 when x = 1

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  11. Solve: y^2 + (x - 1/y)(dy)/(dx) = 0.

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  12. The position vectors of the points A and B are 2 veca + vecb and veca...

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  13. Evaluate: underset(0)overset(pi)int |sinx + cosx|dx

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  14. evaluate underset(0)overset(1)int e^(-x) dx

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  15. A packet, of 10 electronic components is known to include 3 defectives...

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  16. A random variable x follows binomial distribution with mean 3 and stan...

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  17. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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  18. answer any two questions :(iii) if the straight line lx+my=n be a norm...

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  19. Find the vector equation of a line which passes throught the point wit...

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  20. Let vec n be a vector of magnitude 2sqrt 3 such that it makes equal ac...

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