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From a Point A , common tangents are drawn to the circle x^2 + y^2 =a^2/2. And parabola y^2=4ax. Find the area of quadrilateral formed by the common tangents , the chord of contact of circle and chord of contact of parabola. Please explain with steps.

From a Point A , common tangents are drawn to the circle x^2 + y^2 =a^2/2. And parabola y^2=4ax. Find the area of quadrilateral formed by the common tangents , the chord of contact of circle and chord of contact of parabola. Please explain with steps.

Grade:12

1 Answers

Saumya khandelwal
11 Points
4 years ago
Equation of tangent y=mx+a/m Distane of this line from the given circle= radius=a/√2So,|a/m|÷(1+m^2)^0.5 =a/√2Solving we get m=+-1Now line is y=x+a and y= -x-aFind its intersection point with both circle and parabola a trapezium will be form.Find its area by 0.5(sum of parallel sides)*height

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