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Find the locus of the point of intersection of lines {x}{{}}+{

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Find the locus of the point of intersection of lines $x cos α + y sin α = a$ and $x sin α - y cos α = b (α$ is a variable).

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Find the locus of the point of intersection of lines

x cos α + y sin α = a

and

x sin α - y cos α = b (α

is a variable).

7 mins ago

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Practice questions from similar books

Question 1

Consider two straight lines, each of which is tangent to both the circle

x^{2} + y^{2} = \frac{1}{2}

and the parabola

y^{2} = 4 x

. Let these lines intersect at the point

Q

. Consider the ellipse whose center is at the origin

O (0, 0)

and whose semi-major axis is

O Q

. If the length of the minor axis of this ellipse is

2

, then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is

\frac{1}{2}

and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is

\frac{1}{2}

and the length of the latus rectum is

\frac{1}{2}

x = \frac{1}{2}

and

x = 1

\frac{1}{4 2} (π - 2)

(d) The area of the region bounded by the ellipse between the lines

x = \frac{1}{2}

and

x = 1

\frac{1}{16} (π - 2)

View solution

Question 2

Consider the circle

x^{2} + y^{2} = 9

and the parabola

y^{2} = 8 x

. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.

View solution

Question 3

Consider two curves

C 1 : y^{2} = 4 x

;

C 2 = x^{2} + y^{2} - 6 x + 1 = 0

. Then, a. C1 and C2 touch each other at one point b. C1 and C2 touch each other exactly at two point c. C1 and C2 intersect(but do not touch) at exactly two point d. C1 and C2 neither intersect nor touch each other

View solution

Question 4

Match the conditions/expressions A. Two intersecting circles B. Two mutually external circles C. Two circles, one strictly inside the other D. Two branches of a hyperbola

View solution

Question Text

Find the locus of the point of intersection of lines

x cos α + y sin α = a

and

x sin α - y cos α = b (α

is a variable).

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Find the locus of the point of intersection of lines xcosα+ysinα=a and xsinα−ycosα=b(α is a variable).

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Practice questions from similar books

Find the locus of the point of intersection of lines $x cos α + y sin α = a$ and $x sin α - y cos α = b (α$ is a variable).