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Prove that the locus of the point of int...

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola `x^(2)-y^(2)=a^(2)" is " a^(2)(y^(2)-x^(2))=4x^(2)y^(2)`.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  2. Consider the family ol circles x^2+y^2=r^2, 2 < r < 5 . If in the fir...

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  3. Prove that the locus of the point of intersection of the tangents at t...

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  4. If a point (x1,y1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1...

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  5. Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and le...

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  6. Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four poi...

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  7. Find the coordinates of the foci  and the centre of the hyperbola ((...

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  8. show that the area of the triangle inscribed in the circle x^(2)/a^(2)...

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  9. Number of points from where perpendicular tangents can be drawn to the...

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  10. On which curve does the perpendicular tangents drawn to the hyperbola ...

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  11. The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+...

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  12. Statement 1 : The equations of tangents to the hyperbola 2x^2-3y^2=...

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  13. P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot ...

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  14. If P=(x , y),F1=(3,0),F2=(-3,0), and 16 x^2+25 y^2=400 , then P F1+P F...

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  15. Statement 1 : Every line which cuts the hyperbola x^2/4-y^2/16=1 at ...

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  16. Find the equation of the hyperbola whose foci are (8,3)a n d(0,3) and ...

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  17. The number of values of c such that the straight line y=4x+c touches t...

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  18. Find the equation of tangents to the curve 4x^2-9y^2=1 which are paral...

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  19. Statement 1 : The asymptotes of hyperbolas 3x+4y=2 and 4x-3y=5 are the...

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  20. The line passing through the extremity A of the major exis and extremi...

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