Three points A, B, C are taken on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) wi...

Channel:
PW Solutions
Subscribers:
453,000
Published on ● Video Link: https://www.youtube.com/watch?v=v6qY45EZ4m8


Duration: 13:01
0 views
0

Three points A, B, C are taken on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) with eccentric angles \( \theta, \theta+\alpha, \theta+2 \alpha \) is, then
(a) The area of \( \triangle A B C \) is independent of \( \theta \)
(b) The area of \( \triangle A B C \) is independent of \( \alpha \)
(c) The maximum value of area is \( \frac{3 \sqrt{3}}{4} a b \)
(d) The maximum value of area is \( \frac{3 \sqrt{3}}{2} a b \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03The line \( y=x+1 \) meets the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{2}=1 \) at two points \( ...
2023-07-03The acute angle between the pair of tangents drawn to the ellipse \( 2 x^{2}+3 y^{2}=5 \) from t...
2023-07-03Comprehension \( \quad \) Common tangents are drawn to \( C_{1}: x^{2}+y^{2}=16 \) and \( C_{2}:...
2023-07-03Let the eccentricity of an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, ab \), be \( \f...
2023-07-03If \( m \) is the slope of a common tangent to the curves \( \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 ...
2023-07-03A ray emanating from the point \( (-4,0) \) is incident on the ellipse \( 9 x^{2}+25 y^{2}=225 \...
2023-07-03If the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) meets the line \( \frac{x}{7}+\fr...
2023-07-03Comprehension Consider an ellipse \( E: \frac{x^{2}}{16}+\frac{y^{2}}{12} \) \( =1 \) and a para...
2023-07-03If \( \theta \) is acute angle of intersect between two curves \( x^{2}+5 y^{2} \) \( =6 \) and ...
2023-07-03If \( N \) is the foot of the perpendicular drawn from any point \( P \) on the ellipse \( \frac...
2023-07-03Three points A, B, C are taken on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) wi...
2023-07-03The normal at a variable point \( P \) on ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \...
2023-07-03Comprehension \( \quad \) Common tangents are drawn to \( C_{1}: x^{2}+y^{2}=16 \) and \( C_{2}:...
2023-07-03Comprehension For the ellipse \( 2 x^{2}-2 x y+4 y^{2}- \) \( (3+\sqrt{2})=0 \). The inclination...
2023-07-03In triangle \( A B C, a=4 \) and \( b=c=2 \sqrt{2} \). A point \( P \) moves within the triangle...
2023-07-03Comprehension \( \quad \) Common tangents are drawn to \( C_{1}: x^{2}+y^{2}=16 \) and \( C_{2}:...
2023-07-03A ine \( \ell \) is tangent to both the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \) and the...
2023-07-03An ellipse in the first quadrant is tangent to co-ordinate axes. If one focus is \( F_{1}(3,7) \...
2023-07-03If \( x^{2}+4 y^{2}-4=0 \) and minimum and maximum values of \( x^{2} \) \( +y^{2}-x y \) are \(...
2023-07-03Tle tangent and normal at a point \( P \) on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{...
2023-07-03F and \( Q \) are two points on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) whos...