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At the point `(x_(1),y_(1))` on the curve `x^(3)+y^(3)=3axy` show that the tangent is `(x_(1)^(2)-ay_(1))x+(y_(1)^(2)-ax_(1))y=ax_(1)y_(1)`

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At a point (x_1,y_1) on the curve x^3+y^3=3axy , show that the tangent is (x_1^2-ay_1)x+(y_1^2-ax_1)y=ax_1y_1 .

If the tangent at (x_(0),y_(0)) to the curve x^(3)+y^(3)=a^(3) meet the curve again at (x_(1)y_(1)) prove that (x_(1))/(x_(0))+(y_(1))/(y_(0))=-1

If PQ, PR are tangents from a point P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 show that the circumcircle of the triangle PQR is (x-x_(1))(x+g)+(y-y_(1))(y+f)=0

Show that the tangent at P(x_(1),y_(1)) on the curve sqrt(x)+sqrt(y)=sqrt(a) " is " x""x_(1)^((-1)/2)+yy_(1)^((-1)/2)=a^(1/2)

Prove that the area of the triangle formed by the tangents at (x_(1),y_(1)),(x_(2)) "and" (x_(3),y_(3)) to the parabola y^(2)=4ax(agt0) is (1)/(16a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))| sq.units.

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that (h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)) .

AAKASH SERIES-TANGENT AND NORMAL -EXERCISE 7.1 (SHORT ANSWER & LONG ANSWER QUESTIONS)
  1. Find the slopr of the tangent to the curve y=(x-1)/(x-2) at x ne 2 " a...

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  2. Find the slope of the tangent to the curve y = 3x^(4) – 4x at x = 4.

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  3. Find the equation of tangent and normal to the curve y = "2.e" ^((-x)...

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  4. If the slope of the tangent to the curve x^(2)-2xy+4y=0 at the point i...

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  5. Find the equations of tangent and normal to the following curves at th...

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  6. Find the equations of tangent and normal to the following curves at th...

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  7. Find the equations of tangent and normal to the following curves at th...

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  8. Find the equations of tangent and normal to the following curves at th...

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  9. Find the equations of tangent and normal to the following curves at th...

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  10. Find the equations of tangent and normal to the following curves at th...

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  11. If the slope of the tangent to the curve y= x log x at a point on it i...

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  12. Find the equation of tangent and normal to the curve y=x^(3)+4x at (-1...

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  13. Find the equations of tangent and normal to the curve xy = 10 at (2 , ...

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  14. Show that the curves x^(2)+y^(2)=2, 3x^(2)+y^(2)=4x have a common tang...

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  15. IF the tangent at a point on the curve x^(2//3)+y^(2//3)=a^(2//3) inte...

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  16. At what points on the curve x^(2)-y^(2)=2. The slops of tangents are e...

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  17. Show that the tangent at P(x(1),y(1)) on the curve sqrt(x)+sqrt(y)=sqr...

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  18. IF the tangent at any point P on the curve x^my^n=a^(m+n), mn ne 0 mee...

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  19. Show that the tangent at the point P(2,-2) on the curve y(1-x)=x makes...

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  20. At the point (x(1),y(1)) on the curve x^(3)+y^(3)=3axy show that the t...

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