If The Equation 5x 12+5y 22=λ2 2λ+13x+4y 12 Represents An Ellipse ...

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If the equation (5x−1)2+(5y−2)2=(λ2−2λ+1)(3x+4y−1)2 represents an ellipse, then

Aλ∈(0,2)−{1}Right on! Give the BNAT exam to get a 100% scholarship for BYJUS coursesBλ∈(0,2)No worries! We‘ve got your back. Try BYJU‘S free classes today!Cλ∈(0,1)No worries! We‘ve got your back. Try BYJU‘S free classes today!Dλ∈(0,1] No worries! We‘ve got your back. Try BYJU‘S free classes today!Open in AppSolution

The correct option is A λ∈(0,2)−{1}Given equation of ellipse is (x−15)2+(y−25)2=(λ−1)2[3x+4y−1√32+42]2 ⇒√(x−15)2+(y−25)2=|(λ−1)||3x+4y−1|√32+42 It represents an ellipse with focus at (15,25) and directrix as 3x+4y−1, then eccentricity lies in (0,1) ⇒0<|λ−1|<1⇒−1<λ−1<1∴λ∈(0,2)−{1}

flagSuggest Correctionsthumbs-up6similar_iconSimilar questionsQ. If the equation (5x−1)2+(5y−2)2=(λ2−2λ+1)(3x+4y−1)2 represents an ellipse, thenQ. If any point P(x,y) satisfies the relation represents parabola, then (5x−1)2+(5y−2)2=λ(3x−4y−1)2Q. Show that the equation (10x−5)2+(10y−5)2=(3x+4y−1)2 represents an ellipse. Find the length of its latus rectum.Q. The equation (13x−1)2+(13y−1)2=k(5x−12y+1)2 will represent a parabola ifQ. The equation of auxiliary circle of the ellipse 16x2+25y2+32x−100y=284 isView MoreJoin BYJU'S Learning ProgramGrade/Exam1st Grade2nd Grade3rd Grade4th Grade5th Grade6th grade7th grade8th Grade9th Grade10th Grade11th Grade12th GradeSubmitexplore_more_iconExplore moreDefinition of EllipseStandard XIII MathematicsJoin BYJU'S Learning ProgramGrade/Exam1st Grade2nd Grade3rd Grade4th Grade5th Grade6th grade7th grade8th Grade9th Grade10th Grade11th Grade12th GradeSubmitbook_imageAI Tutorbook_imageTextbooksbook_imageQuestion Papersbook_imageInstall appCrossIcon

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