For \( t \in(0,2 \pi) \), if \( A B C \) is an equilateral triangle with vertices \( A(\sin t,-\...

Channel:
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=109ecIpArbc



Duration: 9:25
2 views
0


For \( t \in(0,2 \pi) \), if \( A B C \) is an equilateral triangle with vertices \( A(\sin t,-\cos t), \mathrm{B}(\cos t, \sin t) \) and \( C(a, b) \) such that its othocentre lies on a cricle with centre \( (1,1 / 3) \), then \( \left(a^{2}-b^{2}\right) \) is equal to
(a) \( 8 / 3 \)
(b) 8
(c) \( 77 / 9 \)
(d) \( 80 / 9 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-07-03If two distinct chords, drawn from the point \( (p, q) \) on the circle \( x^{2}+y^{2}=p x+q y( ...
2023-07-03The angle between a pair of tangents drawn from a point \( P \) to the circle \( x^{2}+y^{2}+4 x...
2023-07-03Let \( C \) be a circle passing through the points \( A(2,-1) \) and \( B(3 \), 4). The line seg...
2023-07-03A circle touches both the \( y \)-axis and the line \( x+y=0 \). Then the locus of its center is...
2023-07-03A circle \( C_{1} \) passes through the origin \( O \) and has diameter 4 on the positive \( x \...
2023-07-03If the tangents drawn at the points \( O(0,0) \) and \( P(1+\sqrt{5}, 2) \) on the cirlce \( x^{...
2023-07-03The set of values of \( k \), for which the circle \( C: 4 x^{2}+4 y^{2}-12 x+8 y+k=0 \) lies in...
2023-07-03Let a circle \( C \) touch the lines \( L_{1}: 4 x-3 y+K_{1}=0 \) and \( L_{2}: 4 x-3 y+K_{2}=0,...
2023-07-03Let the tangent to the circle \( \mathrm{C}_{1} x^{2}+y^{2}=2 \) at the point \( M(-1 \), 1) int...
2023-07-03Let a triangle \( A B C \) be inscribed in the circle \( x^{2}-\sqrt{2}(x+y)+y^{2}=0 \) such tha...
2023-07-03For \( t \in(0,2 \pi) \), if \( A B C \) is an equilateral triangle with vertices \( A(\sin t,-\...
2023-07-03If the circle \( x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R} \) passes throught the point ...
2023-07-03Let \( C \) be the centre of the circle \( x^{2}+y^{2}-x+2 y=\frac{11}{4} \) and \( \mathrm{P} \...
2023-07-03Let the abscissae of the two points \( P \) and \( Q \) on a circle be the roots of \( x^{2}-4 x...
2023-07-03Let the tangents at two \( A \) and \( B \) on the circle \( x^{2}+y^{2}-4 x+3 \) \( =0 \) meet ...
2023-07-03Let a circle \( \mathrm{C}:(x-h)^{2}+(y-k)^{2}=r^{2}, k0 \), touch the \( x \)-axis at \( (1,0) ...
2023-07-03The line \( l x+m y+n=0 \) intersects the curve \( a x^{2}+2 h x y+ \) \( b y^{2}=1 \) at the po...
2023-07-03Let a circle \( C \) touch the lines \( L_{1}: 4 x-3 y+K_{1}=0 \) and \( L_{2}: 4 x-3 y+K_{2}=0,...
2023-07-03A circle touches both the \( y \)-axis and the line \( x+y=0 \). Then the locus of its center is...
2023-07-03Let \( 2 x^{2}+y^{2}-3 x y=0 \) be the equation of a pair of tangents drawn from the origin \( O...
2023-07-03The value of \( k \) for which the point \( (2 k+1, k-1) \) is an interior point of the smaller ...