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Show that the four straight lines xcosal...

Show that the four straight lines `xcosalpha+ysinalpha=P`,`xsinalpha-ycosalpha=-p`and `xsinalpha-ycosalpha=P`form a square.

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Show that the sum of the squares of the perpendiculars from the origin upon the lines xcosalpha+ysinalpha=acos2alphaandxsecalpha+ycossecalpha=2a is independent of alpha .

Find the locus of the point of intersection of lines xcosalpha+ysinalpha=a and xsinalpha-ycosalpha=b(alpha is a variable).

Show that the equation of straight line xcosalpha+ysinalpha=p can be expressed in the following form : (x-pcosalpha)/-sinalpha=(y-p sinalpha)/cosalpha=r

Show that the equation of the straight line xcosalpha+ysinalpha=p can be expressed in the following form: (x-pcosalpha)/(-sinalpha)=(y-p sin alpha)/(cosalpha)=r

Show that the four straight lines 5x-y=6, x+5y-22=0,5x-y-32=0and x+5y+4=0 form a square.

If the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, then prove that p^2=4a^2cosalphasinalphadot

Line a x+b y+p=0 makes angle pi/4 with xcosalpha+ysinalpha=p ,p in R^+ . If these lines and the line xsinalpha-ycosalpha=0 are concurrent, then

Find the area of the triangle formed by the straight lin x cosalpha+ysinalpha=P and two coordinates axis.

Show that DeltaH = q//p .

Find the area of the triangle formed by the straight line xcosalpha+ysinalpha=p with the axes of coordinates.

UNITED BOOK HOUSE-MCQ-EXERCISE
  1. If Sn be the sum of n consecutive terms of an A.P. show that S(n+4)-4S...

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  2. If n th term of a-series be (2.3^(n-1)+1),, find the sum of 1st r ter...

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  3. Show that the four straight lines xcosalpha+ysinalpha=P,xsinalpha-ycos...

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  4. Applying section formulae show that the points A(4. 7,-6), B (2, 5, -4...

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

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  6. Evaluate:lim(xrarr0)(sqrt(1+x^2)-sqrt(1+x))/(sqrt(1+x^3)-sqrt(1+x))

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  7. Evaluate: underset(x rarr 0)(lim)(e^(3x)-1)/(log(1+5x))

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  8. Evaluate :lim(xrarrpi//2)(xtanx-pi/2 secx)

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  9. Water is following into a right circular conical vassel. 45 cm deep an...

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  10. if y=f{f(x)},f(0)=0and f'(0)=5 find [dy/dx](x=0)

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  11. Find the coefficient of variation of the following data :

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  12. Find the mean deviation about median from the following data.

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  13. For any two events A and B prove that P(A cup B) le P{A) + P (B).

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  14. From 100 tickets numbered 1, 2,3.. ..... 100.four are drawn at random....

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  15. Two balls are drawn at random from a bag containing 6 white and 4 blac...

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  16. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

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  17. If acosphi=b costheta,show that a tantheta+b tanphi=(a+b)tan((theta+ph...

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  18. If (cot(alpha-beta))/cotalpha+(cos^2gamma)/(cos^2alpha)=1show that tan...

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  19. Solve :cos^3xcos3x+sin^3xsin3x=0

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  20. In any triangle ABC If sinA : sinB: sinC=4:5:6,then prove that cos A ...

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