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If ax^2+2hxy+by^2+2gx+2fy+c=0 represents...

If `ax^2+2hxy+by^2+2gx+2fy+c=0` represents two parallel lines then prove that `h^2=ab`.

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If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that af^2=bg^2 .

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that the distance between the parallel lines is 2sqrt((g^2-ac)/(a(a+b)))" or "2sqrt((f^2-bc)/(b(a+b))) .

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of lines then prove that triangle=abc+2fgh-af^2-bg^2-ch^2=0 .

SRISIRI PUBLICATION-QUESTION PAPER -SECTION - C
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  2. Find the centroid and the area of the triangle formed by the lines 12x...

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  3. If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove...

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  4. If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove...

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  5. If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove...

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  6. Find the angle between the lines joining the origin to the points of i...

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  7. Find the value if k , if the lines joining the origin with the points ...

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  8. Show that the lines joining the origin with the points of intersection...

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  9. Find the condition for the chord lx + my=1 of the circle x^(2)+y^(2)=a...

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  10. Find the angle between the lines whose d.c's are related by l + m + n ...

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  11. Find the direction cosines of the two lines which are connected by the...

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  12. Find the angle between the lines, whose direction cosines are given by...

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  13. If a line makes angles alpha, beta, lambda,delta with the four diagon...

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  14. If y=Tan^""(-1)((sqrt((1+x^(2)))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-...

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  15. Find the derivative of (sinx)^(log x)+x^(sinx).

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  16. Find the derivative of x^(tanx)+(sinx)^(cosx) w.r.to x.

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  17. if siny=xsin(a+y) then show that dy/dx=sin^(2)(a+y)/(sina).

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  18. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

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  19. If x^(y) + y^(x) = a^(b) then prove that (dy)/(dx)=-[(yx^(y-1)+y^(x)L...

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  20. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) then prove that dy/dx=(sqrt(1-y^...

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