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Let P and Q be distinct points on the pa...

Let P and Q be distinct points on the parabola `y^2 = 2x` such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle `Delta OPQ` is `3 sqrt 2` , then which of the following is (are) the coordinates of `P?`

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...

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  2. Let L be a normal to the parabola y^2=4x dot If L passes through the p...

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  3. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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  4. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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  5. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=...

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  6. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn ...

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  7. If y+3=m1(x+2) and y+3=m2(x+2) are two tangents to the parabola y2=8...

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  8. A line of slope lambda(0 lt lambda lt 1) touches the parabola y+3x^2=...

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  9. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to...

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  10. The straight lines joining any point P on the parabola y^2=4a x to the...

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  11. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  12. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

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  13. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) ...

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  14. From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the...

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  15. A line A B makes intercepts of lengths a and b on the coordinate axes....

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  16. Prove that the line joining the orthocentre to the centroid of a tr...

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  17. A is a point on the parabola y^2=4a x . The normal at A cuts the parab...

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  18. The equation of the line that touches the curves y=x|x| and x^2+(y-2)^...

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  19. Let PQ be a chord of the parabola y^2=4x. A circle drawn with PQ as a...

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  20. Statement 1: Through (lambda,lambda+1) , there cannot be more than one...

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