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The sum of the distance of a moving point from the points (4,0) and (-4,0) is always 10 units. Find the equation to the locus of the moving point.

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i. Find the coordinates of the point which trisect the line segment joining the points P(4,0,1) and Q(2,4,0) . (ii) Find the locus of the set of points P such that the distance from A(2,3,4) is equal to twice the distance from B(-2,1,2) .

FULL MARKS-MODEL TEST PAPER-PART-IV
  1. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  2. Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by usi...

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  3. The sum of the distance of a moving point from the points (4,0) and (-...

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  4. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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  5. Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec...

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  6. Evaluate int (cos2x)/((sin x + cos x)^(2))dx.

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  7. Evaluate int sin^(-1) xdx.

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  8. Evaluate Lim(x rarr pi/4) (4sqrt(2)-(cos x + sin x)^(5))/(1-sin 2 x)

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  9. Suppose the chances of hitting a target by a person X is 3 times in 4 ...

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  10. Find the range of the function (1)/(2cosx-1).

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  11. If the equations x^(2) - ax + b = 0 and x^(2) - ex + f = 0 have one ro...

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  12. Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=...

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  13. Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1 ...

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  14. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  15. Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by usi...

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  16. The sum of the distance of a moving point from the points (4,0) and (-...

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  17. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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  18. Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec...

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  19. Evaluate int (cos2x)/((sin x + cos x)^(2))dx.

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  20. Evaluate int sin^(-1) xdx.

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