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Find the position of points P(1,3) w.r.t...

Find the position of points P(1,3) w.r.t. parabolas `y^(2)=4x and x^(2)=8y`.

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We have parabolas `y^(2)-4x=0andx^(2)-3y=0`.
Let `S^(1)-=y^(2)-4xandS_(2)-=x^(2)-3y`
Now, `S_(1)(1,3)=3^(2)-4(1)gt0`
And `S_(2)(1,3)=1^(2)-3(3)lt0`
Thus, (1,3) lies in the exterior region of the parabola `y^(2)=4x` and interior region of the parabola `x^(2)=3y`.
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CENGAGE-PARABOLA-Question Bank
  1. Find the position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)...

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  2. If (alpha, beta) is a point on parabola y^2=4 x which is nearest to th...

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  3. The, focall chord of the parabola (y-2)^2=16(x-1) is a tangent to the ...

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  4. A chord P Q is a normal to the y^2=4 a x at P and subtendsa right ang...

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  5. If radius of circle passing through the focus of parabola x^2=4 y and ...

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  6. The equation of latus rectum of a parabola is x+y=8 and cquation of th...

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  7. Normals of parabola y^2=4 x at P and Q meet at R(x2, 0) and tangents a...

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  8. Chord of the curve 3 x^2-y^2-2 x+4 y=0, which subtends a right angle a...

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  9. If the equation lambda(4 x-3)^2+4(2 y-7)^2right=mu(4 x-3 y+3)^2 repres...

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  10. Tangents are drawn from any point.on directrix of y^2=16 x to parabola...

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  11. Absoulte value of y -intercept of the common tangent to the parabola y...

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  12. Let y=x+1 be the axis of parabola, y+x-4=0 be the tangent of same para...

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  13. Let the parabola y=a x^2+b x+c has vertex at M(4,2) and a in[1,3] . If...

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  14. From the point (4,6), a pair of tangent lines is drawn to the parabola...

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  15. If the normal to a parabola y^2=4 a x at P meets the curve again in Q ...

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  16. A circle is drawn to pass through the extremities of the latus rectum ...

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  17. If (-2,7) is the highest point on the graph of y=-2 x^2-4 a x+k, ...

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  18. The tangent at P(1,2) to the parabola y^2=4 x meets the tangent at ver...

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  19. If three normals are drawn from the point (6,0) to the parabola y^2=4 ...

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  20. Square of the area of the triangle formed by end points of a focal cho...

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  21. Let S be the set all points (x, y) satisfying y^2 le 16 x . For points...

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