Question 45 of 70beginner🔧 ApplyShort Answer2 marks

In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

Correct Answer

The equation of the ellipse is x225+y29=1\frac{x^2}{25} + \frac{y^2}{9} = 1.

Exercise: EXERCISE 10.3 | Q: 18 | (Page 20)
For More Understanding

Explanation

This question tests the student's understanding of the relationship between the parameters of an ellipse. The key relation c² = a² - b² connects the semi-major axis (a), semi-minor axis (b), and the distance of foci from centre (c). Since foci are on the x-axis, the standard form with major axis along x-axis is used.

Solution Steps

  1. Step 1: Since the foci are on the x-axis and centre is at origin, the equation of ellipse is of the form x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.

  2. Step 2: Given b = 3 and c = 4. Using the relation c² = a² - b², we get 16=a2−916 = a^2 - 9.

  3. Step 3: Solving for a²: a2=16+9=25a^2 = 16 + 9 = 25.

  4. Step 4: Substituting a² = 25 and b² = 9 in the standard equation, we get x225+y29=1\frac{x^2}{25} + \frac{y^2}{9} = 1.

PreviousNext