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Find the condition for the two concen...

Find the condition for the two concentric ellipses `a_1x^2+\ b_1y^2=1\ a n d\ a_2x^2+\ b_2y^2=1` to intersect orthogonally.

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RD SHARMA ENGLISH-TANGENTS AND NORMALS-All Questions
  1. Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at th...

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  2. Find the condition for the following set of curves to intersect ort...

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  3. Find the condition for the two concentric ellipses a1x^2+\ b1y^2=1\...

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  4. Show that the curves (x^2)/(a^2+lambda1)+(y^2)/(b^2+lambda1)=1 and (x^...

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  5. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  6. Find the point on the curve y=x^2-2x+3 , where the tangent is pa...

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  8. If the tangent line at a point (x ,\ y) on the curve y=f(x) is para...

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  9. Write the value of (dy)/(dx) , if the normal to the curve y=f(x) at...

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  10. If the tangent to a curve at a point (x ,\ y) is equally inclined t...

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  11. If the tangent line at a point (x ,\ y) on the curve y=f(x) is para...

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  12. Find the slope of the normal at the point ' t ' on the curve x=1/t ...

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  13. Write the coordinates of the point on the curve y^2=x where the tan...

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  14. Write the angle made by the tangent to the curve x=e^tcost , y=e^tsi...

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  15. Write the equation of the normal to the curve y=x+sinxcosx at x=pi/...

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  16. Find the coordinates of the point on the curve y^2=3-4x where tange...

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  17. Write the equation of the tangent to the curve y=x^2-x+2 at the poin...

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  19. Write the angle between the curves y=e^(-x) and y=e^x at their poin...

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