WebThe given equation of latus rectum is y + 5 = 0 or y = -5. The focus of parabola having latus rectum y = -a is (0, a), and the equation of parabola is x2 = 4ay x 2 = 4 a y. The required equation of parabola is x2 = 4(5)y x 2 = 4 ( 5) y. Therefore the required equation of a parabola is x2 = 20y x 2 = 20 y. WebApr 6, 2024 · The latus rectum is a line that runs parallel to the conic's directrix and passes through its foci. The focal chord is the Latus rectum, and the number of latus rectums …

9.1.1E: Ellipses (Exercises) - Mathematics LibreTexts

WebLatus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose endpoints lie on the ellipse as shown below. Let’s find the length of … WebThe equation of an ellipse is ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , {\displaystyle {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1,} where ( h , k ) is the center of the ellipse in … openfpga analogue pocket

The equation of the latus rectum of the ellipse $9{{x}^{2}}+4

WebJan 27, 2024 · We know that the endpoints on the Latus Rectum are L (a,2a) and L’ (a,-2a). Hence, to find the length of the Latus Rectum, all we have to do is find the distance between the points L and L’. Using Distance Formula, the length LL’ is → → √[(a−a)²+2a−(−2a)²] [ ( a − a) ² + 2 a − ( − 2 a) ²] → → [0 + {2a + 2a} 2] → → [4a 2] → ± … WebMar 29, 2024 · In this question, we have been asked to find the equation of latus rectum of the ellipse having equation $9{{x}^{2}}+4{{y}^{2}}-18x-8y-23=0$. We know that to find the equation of latus rectum, we should know the equation of ellipse is $\dfrac{{{\left( x-4 \right)}^{2}}}{{{a}^{2}}}+\dfrac{{{\left( y-k \right)}^{2}}}{{{b}^{2}}}=1$. We will ... WebThe semi-latus rectum is equal to the radius of curvature at the vertices (see section curvature ). Tangent [ edit] An arbitrary line intersects an ellipse at 0, 1, or 2 points, respectively called an exterior line, tangent … open foxit pdf in adobe