The tangent \( P T \) and the normal \( P N \) to the parabola \( y^{2}=4 a x \) at a point \( P....

Channel:
Subscribers:
456,000
Published on ● Video Link: https://www.youtube.com/watch?v=9cETzWBsFL8



Duration: 8:41
1 views
0


The tangent \( P T \) and the normal \( P N \) to the parabola
\( \mathrm{P} \)
\( y^{2}=4 a x \) at a point \( P \) on it meet its axis at points \( T \) and
W
\( N \), respectively. The locus of the centroid of the \( \triangle \) PTN is a parabola whose-
(1) vertex is \( \left(\frac{2 a}{3}, 0\right) \)
(2) directrix is \( x=0 \)
(3) latus rectum is \( \frac{2 a}{3} \)
(4) focus is \( (a, 0) \)
.
(4) (1) (8) (9)


📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2024-01-23The focus of the parabola \( x^{2}-\lambda y+3=0 \) is \( (0,2) \). Match the items of Column I ....
2024-01-23The number of points at which the parabola \( y^{2}=4 \mathrm{x} \) and the circle \( x^{2}+y^{2....
2024-01-23The equation of the ellipse whose foci are \( ( \pm 3,0) \) and eccentricity \( \frac{1}{3} \) i....
2024-01-23Match the items of Column I with those of Column II. \begin{tabular}{|l|l|c|l|} \hline \multicol....
2024-01-23The equation of the common tangents to the parabolas \( x^{2}=y \) and \( (x-2)^{2}=-y \) are- (....
2024-01-23If \( x+y=a \) is normal to the parabola \( y^{2}=12 x \), then the value of \( a \) is equal to....
2024-01-23Consider the circle \( x^{2}+y^{2}=9 \) and the parabola \( y^{2}=8 x \). They intersect at \( P....
2024-01-23Slope of the common tangent of the curves \( y^{2}=8 x \) and \( x y=-1 \) is....
2024-01-23\( P\left(2 t^{2}, 4 t\right) \) is a point on the parabola \( y^{2}=8 x \) and \( Q(h, k) \) is....
2024-01-23Consider the circle \( x^{2}+y^{2}=9 \) and the parabola \( y^{2}=8 x \). They intersect at \( P....
2024-01-23The tangent \( P T \) and the normal \( P N \) to the parabola \( y^{2}=4 a x \) at a point \( P....
2024-01-23Consider the circle \( C: x^{2}+y^{2}-6 y+4=0 \) and the parabola \( P: y^{2}=x \). Then....
2024-01-23If \( C \) is a circle described on the focal chord of the parabola \( y^{2}=4 x \) as diameter ....
2024-01-23\( P\left(2 t^{2}, 4 t\right) \) is a point on the parabola \( y^{2}=8 x \) and \( Q(h, k) \) is....
2024-01-23\( P\left(2 t^{2}, 4 t\right) \) is a point on the parabola \( y^{2}=8 x \) and \( Q(h, k) \) is....
2024-01-23Let \( A \) and \( B \) be two distinct points on the parabola \( y^{2} \) \( =4 x \). If the ax....
2024-01-23In the parabola \( y^{2}=4 x \), the tangent at the point \( P \), whose abscissa is equal to th....
2024-01-23\( P \) is a point on the directrix of the parabola \( y^{2}=4 a x \) and \( Q \) is the point o....
2024-01-23From point \( A \), common tangents are drawn to the circle \( x^{2}+y^{2}=\frac{a^{2}}{2} \) an....
2024-01-23For the parabola \( y^{2}=4 a x \), let \( T=(-a, 0) \). If \( P P^{\prime} \) is a double ordin....
2024-01-23If \( P\left(x_{1}, y_{1}\right) \) and \( Q\left(x_{2}, y_{2}\right) \) are two points on the p....