answer any two questions :(iii) if the s...

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) .

If the straight line lx + my=1 is a normal to the parabola y^(2)=4ax , then-

If the straight line lx+my=n is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 show that (a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2)) .

If the striaht line lx+my=1 is a normal to the parbaola y^(2)=4ax then show that, al^(3)+2alm^(2)=m^(2)

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

Find the coodition that the straight line lx+my+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Find the coodition that the straight line lx+my+n=0 is a normal to the circle x^(2)+y^(2)+2gx+2fy+c=0

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

Find the condition that the straight line lx+my=n touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If the straight line y=my+1 be the tangent of the parabola y^2=4x at the point (1,2), then the value of m will be

UNITED BOOK HOUSE-HIGHER SECONDARY QUESTION 2018-EXERCISE

A relation R is defined on the set of natural numbers N as follows: R=...
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answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...
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(b) answer the foll. Questions: (i) express the matrix A=[[3,2,3],[4,5...
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if |[x-1,1,1],[1,x+1,-1],[-1,1,x+1]| =0 , find the value of x.
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answer the foll. Questions: (i) if y=(sin^(-1)x)/(sqrt(1-x^2)) , then ...
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or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...
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answer the foll. Questions: (ii)evaluate :int (x^4+1)/(x^6+1) dx
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or, evaluate :int dx/(cos x+sqrt 3 sin x)
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answer the foll. Question: (iii) solve : x dy/dx = y+x tan (y/x) , giv...
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or , solve:(1-x^2) dy/dx - xy=1 .
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(d) answer any one question : (i) if three vectors vec a, vec b and ve...
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answer any one question : (ii) let vec a= hat i+4 hat j+ 2hat k , vec...
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Evaluate lim(n->oo)[1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3)+…+1...
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answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...
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answer any one question : (ii) if X and Y are two independent variable...
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(b)answer any two questions : (i) a circular ink blot grows at the rat...
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answer any two questions :(iii) if the straight line lx+my=n be a norm...
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answer any two questions :(iv) solve :(2x-10y^3) dy/dx+y=0 .
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answer any one question : (ii) find the equation of the line which is...
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