Home
Class 12
MATHS
If sec alpha and alpha are the roots of ...

If sec `alpha and alpha` are the roots of `x^2-p x+q=0,` then (a) `p^2=q(q-2)` (b) `p^2=q(q+2)` (c)`p^2q^2=2q` (d) none of these

Text Solution

Verified by Experts

The correct Answer is:
Centre `-=(10//3,0); "Radius" = 2//3`
`|(z-2)/(z-3)| =2`
`rArr |z-2|^(2) = 4|z-3|^(2)`
`rArr |x-2+iy|^(2) = 4|x-3+iy|^(2)`
`rArr(x-2)^(2) + y^(2) = 4[(x-3)^(2) +y^(2)]`
`rArr 3x^(2) + 3y^(2) -(20)/(3)x + (32)/(3) =0`
`rArr x^(2) + y^(2) -(20)/(3)x + (32)/(3) = 0`
`rArr (x-(10)/(3))^(2) + y^(2) = (4)/(9)`
Thus,distance of (x,y) from the point (10/3,0) is 2/3.
So,centre of the circle is (10/3,0) and rasius is 2/3.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.7|6 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.8|11 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.5|12 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

If p and q are the roots of the equation x^2+px+q =0, then

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If alphaandbeta be the roots of the equation x^(2)-px+q=0 then, (alpha^(-1)+beta^(-1))=(p)/(q) .

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e n h= a. -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/a-q/p) d. none of these

If p=a+bomega+comega^2 , q=b+comega+aomega^2 , and r=c+aomega+bomega^2 , where a ,b ,c!=0 and omega is the complex cube root of unity, then (a) p+q+r=a+b+c (b) p^2+q^2+r^2=a^2+b^2+c^2 (c) p^2+q^2+r^2=-2(p q+q r+r p) (d) none of these

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha_1,alpha_2 are the roots of equation x ^2-p x+1=0a n dbeta_1,beta_2 are those of equation x^2-q x+1=0 and vector alpha_1 hat i+beta_1 hat j is parallel to alpha_2 hat i+beta_2 hat j , then p= a. +-q b. p=+-2q c. p=2q d. none of these

If the difference of the roots of the equation x^2-px+q=0 is 1, then show that p^2+4q^2= (1+2q)^2 .