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Find the focus of the parabola y=x^2+x+1...

Find the focus of the parabola `y=x^2+x+1`.

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If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

The coordinates of the focus of the parabola 3y^(2) = 8 x are _

If a straight line pasing through the focus of the parabola y^(2) = 4ax intersects the parabola at the points (x_(1), y_(1)) and (x_(2) , y_(2)) then prove that y_(1)y_(2)+4x_(1)x_(2)=0 .

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UNITED BOOK HOUSE-THE SCOTTISH CHURCH COLLEGIATE SCHOOL-EXERCISE
  1. Find the equation of the st.line which pass through the pt(3,1) and pe...

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  2. Show that the locus of the pt of intersection of the st.lines xcosthe...

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  3. Find the focus of the parabola y=x^2+x+1.

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  4. Prove that the derivative of an odd function an ever function .

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  5. Evaluate :lim(xrarry)(cos^2x-cos^2y)/(x^2-y^2)

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  6. If y = sqrt(x+sqrt(x+sqrt(x+* * * infty))) then (dy)/(dx)=

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  7. Prove that Axx(BcupC)=(AxxB)cup(AxxC)

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  8. If cos theta=(acosphi+b)/(a+bcosphi)(theta,phiacute angle)show that ta...

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  9. If (tan3alpha)/(tanalpha)=lambda,show that (sin3alpha)/(sinalpha)=(2la...

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  10. For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/...

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  11. Show that 1 is a root of a(b-c)x^2+b(c-a)x+c(a-b)=0.Hence show that if...

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  12. Find the sum to n terms :1/2+3/2^2+5/2^3+...+(2n-1)/2^n

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  13. Find the term inedpendent of X in the expansion of (1+x)^3(1-1/x)^6

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  14. A moving st.line always passes through a fixed pt.(alpha,beta).Prove t...

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  15. Find the image of the pt.(-3,-1)with respect to the st.line 2x+3y+22=0

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  16. Find equations of all possible circles that touch the y axis at the po...

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  17. Find the equation of the circles which touche the y axes id and passes...

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  18. Show that lim(xrarr1)(1-x)tan((pix)/2)=2/pi

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  19. If 2f(x)+3f(-x)=x^2-x-1,then find f'(1).

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  20. Find from the first principle,the derivative of tan 2x at x=pi/8

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