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The equation 2x2+3y2−8x−18y+35 = λ Represents
- a)the empty set if λ > 0
- b)a circle for all λ
- c)an ellipse if λ < 0
- d)a point if λ = 0
Correct answer is option 'D'. Can you explain this answer?
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The equation2x2+3y2−8x−18y+35 = λ Representsa)the e...
Given the equation is,
2x2+3y2−8x−18y+35=K
Or, 2{x2−4x+4} + 3{y2−6y+9}=K
Or, 2(x−2)2 + 3(y−3)2 =K.
From the above equation it is clear that if K>0 then the given equation will represent an ellipse and for K<0, no geometrical interpretation.
Also if K=0 then the given equation will be reduced to a point and the point will be (2,3).
2x2+3y2−8x−18y+35=K
Or, 2{x2−4x+4} + 3{y2−6y+9}=K
Or, 2(x−2)2 + 3(y−3)2 =K.
From the above equation it is clear that if K>0 then the given equation will represent an ellipse and for K<0, no geometrical interpretation.
Also if K=0 then the given equation will be reduced to a point and the point will be (2,3).
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