Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Differential Equations

Short Answer Type

81. Form the differential equation of the family of circles having centre on x-axis and radius 3 units.

124 Views

Long Answer Type

82. Find the differential equation of all the circles in the first quadrant which touch the co-ordinate axes.

86 Views

83. Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

158 Views

84. Form the differential equation of the family of circles touching the x-axis at origin.

97 Views

Short Answer Type

85. Form the differential equation of the family of circles touching the y-axis at origin.

96 Views

86. Form the differential equation of the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Let P denote the family of given parabolas and let (a, 0) be the 'focus of a member of the given family, where a is an arbitrary constant. Therefore, equation of family P is
y² = 4 a x ...(1)
Differentiating both sides with respect to x, we get
$2 straight y dy over dx space equals space 4 straight a$ ...(2)

Substituting the value of 4 a from equation (2) in equation (1), we get
$straight y squared space equals space open parentheses 2 straight y space dy over dx close parentheses space left parenthesis straight x right parenthesis space space space space or space space space straight y squared minus 2 xy dy over dx space equals space 0$
which is the differential equation of the given family of parabolas.