NCERT Class 11-Math's: Exemplar Chapter –10 Straight Lines Part 5

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Question 14:

The equation of the line passing through and perpendicular to is

(A)

(B)

(C)

(D)

Answer:

(B) is the correct answer. Let the slope of the line be . Then, its equation passing through is given by

Again, this line is perpendicular to the given line whose slope is (Why?) Therefore, we have

or

Hence, the required equation of the line is obtained by putting the value of in , i.e.,

or

Question 15:

The distance of the point from the line is

(A)

(B)

(C)

(D) None of these

Answer:

(A) is the correct answer. The distance of the point from the line is the length of perpendicular from the point to the line which is given by

(B)

Question 16:

The coordinates of the foot of the perpendicular from the point on the line are

(A)

(B)

(C)

(D)

Answer:

(B) is the correct choice. Let be the coordinates of the foot of the perpendicular from the point on the line . Then, the slope of the perpendicular line is . Again the slope of the given line (why?)

Using the condition of perpendicularity of lines, we have

Or

Since lies on the given line, we have,

Solving (1) and (2), we get and . Thus are the required coordinates of the foot of the perpendicular.

Question 17:

The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point . The equation of the line is

(A)

(B)

(C)

(D)

Answer:

(A) Is the correct choice. Let the line make intercept on axis. Then, it makes intercept on axis. Therefore, the equation of the line is given by

It passes through , so, we have

Therefore, the required equation of the line is given by

Question 18:

A line passes through such that its intercept between the axes is bisected at P. The equation of the line is

(A)

(B)

(C)

(D)

Answer:

The correct choice is (D). We know that the equation of a line making intercepts a and b with axis and axis, respectively, is given by

Here we have

which give and . Therefore, the required equation of the line is given by