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Angle of Intersection of Two Curves

ntThe sides o...

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ntThe sides of a triangle touch y2=4ax and two of its angular points lie on y2=4b(x+c). Show that the locus of third angular point is another parabola.n

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Q. The sides of a triangle touch a parabola, and two of its angular points lie on another parabola with its axis in the same direction; prove that the locus of the third angular point is another parabola.

Q. Two straight lines are perpendicular to each other. One of them touches the parabola

y^{2} = 4 a (x + a)

and the other touches

y^{2} = 4 b (x + b) .

Find the locus of point of intersection.

Q. Two straight lines are perpendicular to each other.One of them touches the parabola

y^{2} = 4 a (x + a)

and the other touches

y^{2} = 4 b (x + b)

.The locus of the point of intersection of the two lines is

Q. There are two perpendicular straight lines touching the parabola

y^{2} = 4 a (x + a)

y^{2} = 4 b (x + b)

, then the point of intersection of these two lines lie on the line given by

Q. The locus of the point of intersection of two tangents to the parabola

y^{2} = 4 a x

which make an angle

α

with one another is

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Angle of Intersection of Two Curves

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