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Show that the common tangents to the par...

Show that the common tangents to the parabola `y^2=4x` and the circle `x^2+y^2+2x=0` form an equilateral triangle.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1: In the parabola y^2=4a x , the circle drawn the taking th...

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  2. The vertices A,B, and C of a variable right triangle lie on a parabol...

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  3. Show that the common tangents to the parabola y^2=4x and the circle x^...

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  4. Consider a curve C : y^2-8x-2y-15=0 in which two tangents T1a n dT2 ar...

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  5. Statement 1: The line a x+b y+c=0 is a normal to the parabola y^2=4a x...

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  6. Statement 1: The length of focal chord of a parabola y^2=8x making on ...

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  7. Statement 1: (5x-5)^2+(5y+10)^2=(3x+4y+5)^2 is a parabola. Statement 2...

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  8. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

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  9. If d is the distance between the parallel tangents with positive slop...

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  10. If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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  11. If the parabola y=a x^2-6x+b passes through (0,2) and has its tangent ...

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  12. If the locus of the middle of point of contact of tangent drawn to the...

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  13. The minimum area of circle which touches the parabolas y=x^2+1 and y^2...

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  14. Tangent is drawn to parabola y^(2)-2y-4x+5=0 at a point P which cuts t...

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  15. The point of intersection of the tangents at the ends of the latus ...

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  16. ·If the normals of the parabola y^2=4x drawn at the end points of it...

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  17. From a point A, commont tangents are drawn to the circle x^2 + y^2=8 a...

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  18. The angle between a pair of tangents drawn from a point P to the hyper...

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  19. Three normals with slopes m1, m2 and m3 are drawn from a point P not o...

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  20. Three normals are drawn from the point (c, 0) to the curve y^2 = x. Sh...

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