A point moves such that the sum of the square of the distances from...

Channel:
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=rjTIM2uVap4



Duration: 0:00
119 views
0


A point moves such that the sum of the square of the distances from two fixed straight lines intersecting
\( \mathrm{P} \) at angle \( 2 \alpha \) is a constant. Prove that the locus is an ellipse of eccentricity

W \( \frac{\sqrt{\cos 2 \alpha}}{\cos \alpha} \) if \( \alpha\frac{\pi}{4} \) and \( \frac{\sqrt{-\cos 2 \alpha}}{\sin \alpha} \) if \( \alpha\frac{\pi}{4} \)
πŸ“² PW App Link - https://bit.ly/YTAI_PWAP
🌐 PW Website - https://www.pw.live/




Other Videos By PW Solutions


2023-02-25A straight line \( P Q \) touches the ellipse \( \frac{x^{2}}{a^{2}...
2023-02-25The equations of the transverse and conjugate axes of a hyperbola a...
2023-02-25Find the locus of the mid-points of the chord of the hyperbola \( \...
2023-02-25Find the locus of the point, the chord of contact of the tangents d...
2023-02-25\( \mathrm{P} \) If the normals at \( \left(x_{i}, y\right), i=1,2,...
2023-02-25The chord \( P Q \) of the rectangular hyperbola \( x y=a^{2} \) me...
2023-02-25If \( x \cos \alpha+y \sin \alpha=p \), a variable chord of the hyp...
2023-02-25The transverse axis of a hyperbola is of length \( 2 a \) and a ver...
2023-02-25Prove that the sum of the eccentric angles of the extremities of a ...
2023-02-25Show that the equation of the pair of tangents to the ellipse \( \f...
2023-02-25A point moves such that the sum of the square of the distances from...
2023-02-25If circumcentre of an equilateral triangle inscribed in \( \frac{x^...
2023-02-25If tangent drawn at a point \( \left(t^{2}, 2 t\right) \) on the pa...
2023-02-25Prove that the orhocentre of any triangle formed by three tangents ...
2023-02-25Prove that the equation to the circle, which passes through the foc...
2023-02-25If \( \alpha, \beta \) are eccentric angles of the extremities of a...
2023-02-25Find the locus of extremities of latus rectum of the family of elli...
2023-02-25Find the locus of centre of a tamily of circles passing through the...
2023-02-25From an external point \( P \), tangents are drawn to the parabola;...
2023-02-25Two tangents to the parabola \( y^{2}=8 x \) meet the tangent at it...
2023-02-25Find locus of a point \( P \) if the three normals drawn from it to...