[email protected]

+91-87964 74404

Grade 12Differential Calculus

The parabolas y2=4ax and x2=4by intersect orthogonally at point P(x1,y1) where x1,y1=0 is not possible, then (A)b=a2 (B)b=a3 (C)b3=a2 (D)None of these.

Jayati Sindhu

16 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:

If two parabolas intersect orthogonally, then the tangents at points of intersection must be perpendicular. Lets find points of intersection:

$y^{2}=4ax$ ...(1)

$x^{2}=4by$ ...(2)

Put y from (2) in (1)

$(\frac{x^{2}}{4b})^{2} = 4ax$

$x_{0} = 4a^{1/3}b^{2/3}, 0$

$y_{0} = 4a^{2/3}b^{1/3}, 0$

Let the slope of tangent to parabola (1) & (2) be m₁& m₂respectively.

$m_{1}.m_{2} = -1$

$m_{1} = \frac{2a}{y_{0}}$

$m_{2} = \frac{x_{0}}{2b}$

$\frac{2a}{y_{0}}. \frac{x_{0}}{2b}=-1$

$\frac{a.a^{1/3}.b^{2/3}}{b.b^{1/3}.a^{2/3}} = -1$

$\frac{a^{2/3}}{b^{2/3}} = -1$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions