find the latus rectum of ellipse x2/9+ y2/16 = 1 is
Answers
EXPLANATION.
Equation of ellipse = x²/9 + y²/16 = 1.
General equation of ellipse = x²/a² + y²/b² = 1.
(a) = Centre of an ellipse = C ( 0,0).
(b) = vertex = B ( 0,b) and B' ( 0,-b )
vertex = B ( 0,4 ) and ( 0,-4 ).
(c) Eccentricity = a² = b²( 1 - e² ).
⇒ 9 = 16 ( 1 - e² ).
⇒ 9 = 16 - 16e².
⇒ 9 - 16 = -16e².
⇒ -7 = -16e².
⇒ e² = √7/16.
⇒ e = √7/4 and -√7/4.
(c) = Focus = S ( o, be 0 and S' ( 0,-be ).
Focus = S ( 0,4 X √7/4 ) and S' ( 0, -4 X √7/4 ).
Focus = S ( 0, √7 ) and S' ( 0, -√7 ).
( D ) = Equation of directrix ⇒ y = +b/e and y = -b/e.
Equation of directrix ⇒ y = 4/√7/4 and y = -4/√7/4.
Equation of directrix = y = 16/√7 and y = -16/√7.
(E) = Length of major axis = 2b = 2(4) = 8.
(F) = Length of minor axis = 2a = 2(3) = 6.
(G) = Length of latus rectum = 2a²/b = 2(3)²/4 = 18/4 = 9/2.
MORE INFORMATION.
Equation of ellipse in different forms.
(1) = Point form.
The equation of the tangent to the ellipse x²/a² + y²/b² = 1 at the point ( x₁ , y₁) is ⇒ xx₁/a² + yy₁/b² = 1.
(2) = Slope Form.
If the line y = mx + c touches the ellipse x²/a² + y²/b² = 1 then,
c² = a²m² + b².
Hence, the straight line y = mx ± √a²m² + b² always represent the tangent to the ellipse.
(3) = Parametric Form.
The equation of tangent at any point ( a cos∅ , b sin∅ ) is,
x cos∅/a + y sin∅/b = 1.
Answer:
The answer is very easy -9/2