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If the line x+y=6 is a normal to the par...

If the line x+y=6 is a normal to the parabola `y^(2)=8x` at point (a,b), then the value of a+b is ___________ .

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The correct Answer is:
6
(6) Slope of the line =-1
From the curve,
`(dy)/(dx)=(4)/(y)`
Hence, slope of normal `=-(y)/(4)=-1ory=4`
Putting y=4 in the equation of curve, we have x=2.
Hence, the point is (2,4).
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CENGAGE-PARABOLA-Exercise (Numerical)
  1. The equation of the line touching both the parabolas y^(2)=4xandx^(2)=...

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  2. If the point P(4, -2) is the one end of the focal chord PQ of the para...

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  3. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

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  4. The locus of the midpoints of the portion of the normal to the parabol...

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  5. Consider the locus of center of the circle which touches the circle x^...

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  6. If on a given base BC[B(0,0) and C(2,0)], a triangle is described such...

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  7. PQ is any focal chord of the parabola y^(2)=8x. Then the length of PQ ...

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  8. The length of focal chord to the parabola y^(2)=12x drawn from the poi...

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  9. From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If ...

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  10. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

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  11. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

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  12. If the circle (x-6)^(2)+y^(2)=r^(2) and the parabola y^(2)=4x have max...

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  13. The slope of line which belongs to family (1+ l) x + (1-l)y + 2(1-l) =...

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  14. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

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  15. Normals at (x(1),y(1)),(x(2),y(2))and(x(3),y(3)) to the parabola y^(2)...

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  16. Foot of perpendicular from point P on the parabola y^(2)=4ax to the ax...

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  17. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

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  18. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

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  19. If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)...

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  20. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

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