• Aim
• Apparatus
• Diagram
• Farmula
• Theory :
• Procedure:
• Observations/Table
• Result :
• Calculation : 
• MCQ :
• Short Answer Questions :

Practical Session No. 7

 Ellipse and hyperbola

1) Find the lengths of the major and minor axes, coordinates of vertices, eccentricity, co-ordinates of the foci, equations of directrices and the length of the Latus Rectum of the following conics

𝑖

) 9𝑥𝑥2+16𝑦𝑦2=144, 𝑖 ) 4𝑥𝑥2+25𝑦𝑦2=100

𝑖

) 𝑥𝑥225−𝑦𝑦29=1 𝑖 𝑖𝑖) 𝑦𝑦24−𝑥𝑥29=1

2) Find the equation of ellipse referred to its principal axes with eccentricity 34 and passing through the point (6,4).

3) An ellipse has OB as a semi-major axis, S and S’ are its foci and ∠𝑆𝑆𝑆 𝑆𝑆′ is a right- angle, then find the eccentricity of the ellipse.

4) Find focal distances of the point P􀵫5,4√3􀵯 on the ellipse 16𝑥𝑥2+25𝑦𝑦2=1600.

5) If 𝑒𝑒1 and 𝑒𝑒2 are eccentricities of hyperbolas 𝑥𝑥2𝑎𝑎2−𝑦𝑦2𝑏𝑏2=1 and 𝑦𝑦2𝑏𝑏2−𝑥𝑥2𝑎𝑎2=1

then show that 1𝑒𝑒12+1𝑒𝑒22=1

6) Find the equation of hyperbola whose

i) directrix is 2𝑥𝑥+𝑦𝑦=1 , focus at (1,2) and eccentricity √3.

ii) foci are at (±4 ,0) and the length of its latus rectum is 12 unit.

iii) vertices are ( 0 ,± 2 ) and the foci are at ( 0 ,± 3 ).

7) An interesting property of rectangular hyperbola

Equation of rectangular hyperbola is x y = k (k is non zero constant) …(I)

Tangent is drawn to the curve at point on it whose abscissa is ‘a’.

Therefore point of contact is (a, … )

Slope of tangent = 􁉂𝑑𝑑𝑑𝑑𝑑 􁉀𝑘𝑘𝑥𝑥􁉁􁉃 at point (a, … )

= 􁉀−𝑘𝑘𝑥𝑥2􁉁 at point (a, … )

= −𝑘𝑘𝑎𝑎2 …(II)

Equation of tangent to xy = k at point (a, … ) is (by slope point form)

y - ….. = 􁉀−𝑘𝑘𝑎𝑎2􁉁(x - a)

i.e. a2 (y - …) = -k (x – a)

i.e. …………

i.e. …………

this equation of tangent in terms of double intercept form is

𝑥𝑥2𝑎𝑎 + 𝑦𝑦2𝑘𝑘𝑎𝑎 = 1.

tangent cuts the x – axis at point P and the Y – axis at point Q.

clearly P = (… , 0) and Q = (0, …)

Area of Δ POQ = 12(OP)(OQ)

= 12(….)(….)

= 2k Verify this interesting result for different values of k.

i) xy = 4 at (2, 2) ii) xy = 12 at (-2, -6)

खलील व्हिडीओ त उत्तरे व Solution मिळेल 

Note: तुम्हाला यासारखे  आणखी उत्तर /Answer /Solution-Practical ट्युटोरियल 

पहायचे असल्यास ,आमच्या You-Tube Channel ची  SUBSCRIBE  सदस्यता घ्या जिथे आम्ही नियमित अश्या प्रकारे  सर्व   टुटोरियल पोस्ट करता ....!!!

SUBSCRIBE

सर्व माहिती वाचा आणि मित्रांना आणि गरजू पर्यंत नक्की शेअर करा.