## Vineet Loomba is teaching live on Unacademy Plus

JEE MAIN RANK BOOSTER COURSE MASTERING ELLIPSE FOR JEE MAIN AND ADVANCED PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-JEE MENTOR

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. Youtube, Founder @ vineetloomba.com unacademy Many of my students are pursuing courses in IITs, NITs, BITs etc. Currently running my own Coaching Institute for JEE Main and Advanced Searh vineet loomba unacademy on GOOGLE

JEE MAIN RANK BOOSTER COURSE IMPORTANT PRACTICE PROBLEMS SET-I PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-JEE MENTOR

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example x2 The equation 2r r-5 +1-0 represents an ellipse, if (B) re(2)U(,5) (A) r> 2 (C) r > 5 (D) r <2 2 2 2-r r-5 2 r-2 5-r It represents ellipse when r-2>0.5-r>0and r-2 5-r SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example A latus rectum of an ellipse is a line (A) *passing through a focus (B) through the centr *perpendicular to the major axis (D) "parallel to the minor axis SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example The centre of an ellipse-1 (a>b) is C, P is any point on the ellipse and PN is ordinate of point P and A, A' are the end points of major axis, then the value of AN AN 1S (A) b/a2 PN2 (B) a/b (C) a2 b2 (D)1 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Let P(x, y) is any point on the ellipse. Then AN = a-x,A"N=a+x 2 2 2,,2 2 ,2 ay Since PN2 AN.A ' N Now = a2-x2 PN2 b ANA'N a SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4, 3) and (-1, 4 (A) 15x2+7y2=247 (B) 7x2 +15y2 247 (D) 7x2 +5y2 247 (C) 7x2 +15y2=247 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) The standard form of the ellipse is Since the point (4, 3) and (-1, 4) lie on the ellipse, we have 16 9 a2 , b2 1 16 andh 2 247 247 and b 15 Solving equations (1) and (ii), we find that a 7 2 2 247 247 15 Hence the required equation is 7x2 + 15y2-247. SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example The distance between the directrices of the ellipse-+--l is 24 (A) (B) 5 V5 18 (C) 5 12 ER. VINEET LOOMBA (IIT ROORKEE) SUCCESS IN JEE MAIN AND ADVANCED

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example If minor-axis of ellipse subtend a right angle at its focus then find the eccentricity of ellipse. Sol. b a2 +21 ZBSO S' O 4 ae b 2 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)