Related InterviewSolutions

• The number of points on the ellipse `(x^2)/(50)+(y^2)/(20)=1`from which a pair of perpendicular tangents is drawn to the ellipse `(x^2)/(16)+(y^2)/9=1`is0 (b) 2(c) 1 (d)4
• Tangents are drawn from the points on the line x-y-5=0 ot `x^(2)+4y^(2)=4` . Prove that all the chords of contanct pass through a fixed point
• If radius of the director circle of the ellipse `((3x+4y-2)^(2))/(100)+((4x-3y+5)^(2))/(625) =1` isA. 6B. `sqrt(34)`C. `sqrt(29)`D. `sqrt(26)`
• PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R are `2alpha, 2beta, 2 gamma`, respectively then `tan beta gamma` is equal toA. `cot alpha`B. `cot^(2)alpha`C. `2 cot alpha`D. None of these
• If the chords of contact of tangents from twopoinst `(x_1, y_1)`and `(x_2, y_2)`to theellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`are atright angles, then find the value of `(x_1x_2)/(y_1y_2)dot`
• Tangents are drawn from any point on the circle `x^(2)+y^(2) = 41` to the ellipse `(x^(2))/(25)+(y^(2))/(16) =1` then the angle between the two tangents isA. `(pi)/(4)`B. `(pi)/(3)`C. `(pi)/(6)`D. `(pi)/(2)`
• Prove that the chords of constant of perpendicular tangents to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` touch another fixed ellipse `(x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/((a^(2)+b^(2)))`
• Prove that the chords of contact of pairs of perpendicular tangents to the ellipse `x^2/a^2+y^2/b^2=1` touch another fixed ellipse.A. `(x^(2))/(a^(2))+(y^(2))/(b^(2)) =(1)/((2a^(2)+b^(2)))`B. `(x^(2))/(a^(2))+(y^(2))/(b^(2)) =(2)/((a^(2)-b^(2)))`C. `(x^(2))/(a^(4))+(y^(2))/(b^(4)) =(1)/((a^(2)+b^(2)))`D. `(x^(2))/(a^(2))-(y^(2))/(b^(2)) =(2)/((3a^(2)-b^(2)))`
• Find the equation of the ellipse (referred to itsaxes as the axes of `xa n dy`, respectively) whose foci are `(+-2,0)`andeccentricity is `1/2`
• Find the equation of the ellipse, with major axis along the x-axis and passing through the points `(4, 3)`and `(-1, 4)`.