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Consider a curve ax^(2)+2hxy+by^(2)=1 an...

Consider a curve `ax^(2)+2hxy+by^(2)=1` and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If the product PQ.PR is independent of the slope of the line, then show that curve is a circle.

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ARIHANT MATHS-CIRCLE -Exercise (Subjective Type Questions)
  1. Two straight lines rotate about two fixed points (-a,0) and (a,0) in a...

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  2. The base AB of a triangle is fixed and its vertex C moves such that si...

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  3. Consider a curve ax^(2)+2hxy+by^(2)=1 and a point P not on the curve. ...

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  4. Tangents drawn from the point P(1,8) to the circle x^(2)+y^(2)-6x-4y-1...

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  5. The centres of two circles C(1) and C(2) each of unit radius are at a...

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  6. If P and Q are the points of intersection of the circles x^(2)+y^(2)+3...

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  7. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

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  8. The circle passing through the point ( -1,0) and touching the y-axis ...

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

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  10. The two circles x^2+""y^2=""a x and x^2+""y^2=""c^2(c"">""0) touch eac...

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  11. The locus of the mid-point of the chord of contact of tangents drawn f...

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  12. A tangent PT is drawn to the circle x^(2)+y^(2)=4 at the point P(sqrt3...

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  13. A tangent PT is drawn to the circle x^2 + y^2= 4 at the point P(sqrt3,...

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  14. The length of the diameter of the circle which touches the x-axis at ...

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  15. The circle passing through (1, -2) and touching the axis of x at (3,...

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  16. Circle(s) touching x-axis at a distance 3 from the origin and having a...

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  17. Let C be the circle with centre at (1, 1) and radius = 1. If T is th...

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  18. A circle S passes through the point (0, 1) and is orthogonal to the ci...

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  19. Locus of the image of the point (2, 3) in the line (2x-3y""+""4)""+"...

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  20. The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 a...

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