A parabola is drawn to pass through \( A \) and \( B \) the ends of a diameter of a given circle...

Channel:
PW Solutions
Subscribers:
453,000
Published on ● Video Link: https://www.youtube.com/watch?v=Y2MPgv3OXVU


Duration: 13:16
2 views
0

A parabola is drawn to pass through \( A \) and \( B \) the ends of a diameter of a given circle of radius a, and to have as directrix a tangent to a concentric circle of radius \( \mathrm{b} \); then axes being \( \mathrm{AB} \) and a perpendicular diameter, prove that the locus of the focus of the parabola is \( \frac{x^{2}}{b^{2}}+\frac{y^{2}}{b^{2}-a^{2}}=1 \).
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03The minimum value of \( \left\{(r+5-4|\cos \theta|)^{2}+(r-3|\sin \theta|)^{2}\right\} \) \( \fo...
2023-07-03The sum of diameters of the circles that touch (i) the parabola \( 75 x^{2}=64(5 y-3) \) at the ...
2023-07-03Comprehension. Let \( a_{n}\&b_{n} \) be the arithmetic sequences each with common difference 2 ...
2023-07-03If radius of the director circle of the ellipse \( \frac{(3 x+4 y-2)^{2}}{100}+\frac{(4 x-3 y+5)...
2023-07-03If the line \( y=4+k x, k0 \), is the tangent to the parabola \( y=x-x^{2} \) at the point \( P ...
2023-07-03Let \( l \) be a line which is normal to the curve \( y=2 x^{2}+x+2 \) at a point \( P \) on the...
2023-07-03Suppose \( x \) and \( y \) are real numbers and that \( x^{2}+9 y^{2}-4 x+ \) \( 6 y+4=0 \) the...
2023-07-03\( T P \) and \( T Q \) are tangents to the parabola \( y^{2}=4 a x \) and the normals at \( P \...
2023-07-03The distance between directrix of the ellipse \( (4 x-8)^{2}+16 y^{2}= \) \( (x+\sqrt{3} y+10)^{...
2023-07-03Two tangent lines \( L_{1} \) and \( L_{2} \) are drawn from the point \( (2,0) \) to the parabo...
2023-07-03A parabola is drawn to pass through \( A \) and \( B \) the ends of a diameter of a given circle...
2023-07-03If \( y=m_{1} x+c_{1} \) and \( y=m_{2} x+c_{2}, m_{1} \neq m_{2} \) are two common tangents of ...
2023-07-03In the following gaseous phase first order reaction math xmlns=http://www.w3.org/1998/Math/MathM...
2023-07-03Let \( x=2 t, y=\frac{t^{2}}{3} \) be a conic. Let \( \mathrm{S} \) be the focus and \( B \) be ...
2023-07-03Let \( x^{2}+y^{2}+A x+B y+C=0 \) be a circle passing through \( (0,6) \) and touching the parab...
2023-07-03Prove that the locus of intersections of tangents to the parabola \( y^{2}=4 a x \) which interc...
2023-07-03Molar concentration of a solution in water is 
2023-07-03\( P Q \) is a double ordinate of the parabola \( y^{2}=4 a x \). If the normal at \( P \) inter...
2023-07-03A line \( A B \) makes intercepts of length \( a \) and \( b \) on the coordinate axes. Find the...
2023-07-03A variable tangent to the parabola \( y^{2}=4 a x \) meets the circle \( x^{2}+y^{2}=r^{2} \) at...
2023-07-03Comprehension. Let \( a_{n}\&b_{n} \) be the arithmetic sequences each with common difference 2 ...