Question
Download Solution PDFIf a circle whose centre is (2, 3) touches the line 4x + 3y - 7 = 0, then the radius of the circle is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Center of the circle = (2, 3)
Equation of the line = 4x + 3y - 7 = 0
Formula used:
Distance from a point (x₁, y₁) to a line ax + by + c = 0 is:
Distance = |a x₁ + b y₁ + c| / √(a² + b²)
Calculations:
Substitute (x₁, y₁) = (2, 3) and the line equation 4x + 3y - 7 = 0 into the formula:
Distance = |(4 × 2) + (3 × 3) - 7| / √(4² + 3²)
⇒ Distance = |8 + 9 - 7| / √(16 + 9)
⇒ Distance = |10| / √25
⇒ Distance = 10 / 5
⇒ Distance = 2
∴ The radius of the circle is 2 units.
Last updated on Jun 25, 2025
-> The Staff selection commission has released the SSC CHSL Notification 2025 on its official website on 23rd June 2025.
-> The SSC CHSL Apply Online 2025 has been started and candidates can apply online on or before 18th July.
-> The SSC has released the SSC CHSL exam calendar for various exams including CHSL 2025 Recruitment. As per the calendar, SSC CHSL Application process will be active from 23rd June 2025 to 18th July 2025.
-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government.
-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).
-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.
-> The UGC NET Exam Analysis 2025 for the exam conducted on June 25 is out.