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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`

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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

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Show that the equation of the straight line joining the points (a,b) and (c,d) can be written as (x-a)(y-d)=(x-c)(y-b) .

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If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2cos^2alpha-b^2sin^2alpha=p^2 .

UNITED BOOK HOUSE-HARE SCHOOL-EXERCISE
  1. Evaluate: underset(x rarr 0)(lim)(3^(x)-1)/((4+x)^(1/2)-2)

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  2. What is the probability of obtaining 7 points with the rolling of two ...

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  3. Show that the equation of straight line xcosalpha+ysinalpha=p can be e...

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  4. If G is the G.M between two positive numbers a and b.show that 1/(G^2-...

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  5. Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc),1/(...

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  6. If a1,a2,a3,...,aaare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

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  7. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show...

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  8. Solve :barz=iz^2(z being a complex number)

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  9. if alpha,beta,gamma are in A>P show that cot=(sinalpha-singamma)/(cosg...

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  10. Prove that (1)/(2sin10^(@))-2sin70^(@)=1.

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  11. Prove that 0le3costheta+4sintheta+5le10

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  12. Show that 4(cos^3 10^@+sin^3 20^@)=3(cos10^@+sin20^@)

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  13. If the equation x^2-cx+d=0and x^2-ax+b=0 have a common root,and the ro...

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  14. If alphaand betaare roots of the equation qx^2+px+p=0,show that sqrt(a...

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  15. If z1 and z2 be two complex numbers show that Re(barz1z2)=1/2(z1barz2+...

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  16. Find the sum up to n terms :1+2/3+3/3^2+4/3^3+...

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  17. If x^(1/a)=y^(1/b)=z^(1/c)where a,b,c are in A.P,,than show that x,y,z...

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  18. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

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  19. IF A+B+C=pi,then prove that tan (A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2...

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  20. Prove that secx=2/(sqrt(2+sqrt(2+sqrt(2+2cos8x)))

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