Question 20 of 70beginner🔧 ApplyShort Answer2 marks

In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum: y² = 10x

Correct Answer

The given equation is y² = 10x.

Comparing with standard form: The equation y² = 10x can be compared with the standard form y² = 4ax. Here, 4a = 10, so a = 5/2.

Coordinates of focus: Since the parabola opens to the right (coefficient of x is positive), the focus is at (a, 0) = (5/2, 0).

Axis of the parabola: Since the equation involves y², the axis of symmetry is along the x-axis.

Equation of directrix: The directrix is x = -a, so x = -5/2.

Length of latus rectum: The length of latus rectum = 4a = 10.

Exercise: EXERCISE 10.2 | Q: 5 | (Page 11)
For More Understanding

Explanation

This question asks students to identify key properties of a parabola in standard form. The equation y² = 10x matches the form y² = 4ax where a = 5/2. From the textbook context, Example 5 demonstrates the same process for y² = 8x, showing that for this form: focus is (a, 0), axis is the x-axis, directrix is x = -a, and latus rectum length is 4a.

Solution Steps

  1. Step 1: Compare y² = 10x with standard form y² = 4ax to find 4a = 10, hence a = 5/2

  2. Step 2: Focus coordinates are (a, 0) = (5/2, 0)

  3. Step 3: Axis is along x-axis since equation involves y²

  4. Step 4: Directrix equation is x = -a = -5/2

  5. Step 5: Length of latus rectum = 4a = 10

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