Home
Class 12
MATHS
((y-3)^(2))/(9)-(x-1)^(2)/(16)=1 Which...

`((y-3)^(2))/(9)-(x-1)^(2)/(16)=1`
Which conic section does this equation define? Also find, if they exist,
(i) the center
(ii) the vertex/vertices
(iii) The directrix
(v) the asymptotes
(vi) the eccentricity

Text Solution

AI Generated Solution

To solve the given equation of the conic section and find the required properties, we will follow these steps: ### Given Equation: \[ \frac{(y-3)^2}{9} - \frac{(x-1)^2}{16} = 1 \] ### Step 1: Identify the Conic Section ...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

((x+3)^(2))/(25)+((y-8)^(2))/(100)=1 Which conic section does this equation define? Also find, if they exist, (i) the center (ii) the vertex/vertices (iii) the focus/foci (iv) the directrix (v) the asymtotes (vi) the eccentricity

(y+4)^(2)=-6(x-2) Which conic section does this define? Also find, if they exist, (i) the center (ii) the vertex/vertices (iii) the focus/foci (iv) the directrix (v) the asymtotes (vi) the eccentricity

Find the equation of the parabola with vertex is at (2,1) and the directrix is x=y-1.

Find the equation to the ellipse whose one focus is (2, 1), the directrix is 2x-y+3=0 and the eccentricity is 1/sqrt(2)

The equation of the hyperbola whose focus is (1,2) , directrix is the line x+y+1=0 and eccentricity 3//2 , is

Find the equation to the conic section whose focus is (1, -1), eccentricity is (1/2) and the directrix is the line x-y=3 . Is the conic section an ellipse?

The directrix of a conic section is the line 3x+4y=1 and the focus S is (-2, 3). If the eccentricity e is 1/sqrt(2) , find the equation to the conic section.

Find the equation of the hyperbola whose focus is (1,2), directrix 2x +y = 1 and eccentricity sqrt3.

Find equation of the ellipse whose focus is (1,-1), then directrix the line x-y-3=0 and eccentricity 1/2 is

Find the equation of the ellipse whose eccentricity is 1/2 , the focus is (1,1) and the directrix is x-y+3=0.