Question
Download Solution PDFWhat is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The equation of the parabola having a vertex at the (h,k) and axis along the positive y-axis is (x - h)2 = 4a(y - k)
Calculation:
The equation of the family of parabolas having vertex at origin and axis along the positive y-axis
⇒ (x - 0)2 = 4a(y - 0)
⇒ x2 = 4ay __(i)
Differentiating both sides with respect to x,
⇒ 2x = 4a
⇒ x = 2a
Putting the value of a from (i) in (ii),
⇒ x = 2
⇒ 2xy = x2
⇒ x
∴ The correct option is (2).
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