Question
Show that the circles and touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.
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Question 1
·If the normals of the parabola drawn at the end points of its latus rectum are tangents to the circle , then the value of is Question 2
Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, , (i), , (P), II, , (ii), , (Q), III, , (iii), , (R), IV, , (iv), , (S), If a tangent to a suitable conic (Column 1) is found to be and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)Question 3
Consider two straight lines, each of which is tangent to both the circle and the parabola . Let these lines intersect at the point . Consider the ellipse whose center is at the origin and whose semi-major axis is . If the length of the minor axis of this ellipse is , then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is and the length of the latus rectum is (c) The area of the region bounded by the ellipse between the lines and is (d) The area of the region bounded by the ellipse between the lines and is Question Text | Show that the circles
and
touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact. |